CN1737709A - Method and system for training fuzzy control unit - Google Patents

Abstract

This invention relates to one method to generate relative output through control signals, which comprises the following steps: generating error signals as the function of process and reference signals; generating one control signal to be fed to process device as error signals and parameter adjusting signals; conducting signals to represent minimized number and computing the signals through the process status and control signals pair values; computing correction signals through controlling one set of signals to be minimized into conductive signals; using NN and fuzzy logic processor to compute parameter adjusting signals.

Description

The method and system that is used for training fuzzy control unit

The application be that March 9, application number in 2000 are 00807374.0 the applying date, denomination of invention divides an application for the application for a patent for invention of " according to the method and the hardware architecture of quantum soft calculation control process or deal with data ".

Technical field

The present invention relates generally to the method and the hardware of the data that are used for control procedure or are used for process database, or rather, relate to control procedure and/or comprise the intelligence operation of searching for minimum value.

Method of the present invention is very useful to the minimum value in class value search, especially, to the hardware system of realizing using artificial intelligence with robust, to control non-linear process and/or search database deftly very useful.

Background technology

The output that feedback control system is widely used in dynamic system remains on ideal value, although external disturbance makes dynamic system skew ideal value.For example, by the family expenses heating fireplace of self-operated thermostatic controller control, be exactly an example of feedback control system.The temperature that the self-operated thermostatic controller continuous coverage is indoor, when temperature drops to required minimum temperature when following, self-operated thermostatic controller is opened fireplace.When indoor temperature reached required minimum temperature, self-operated thermostatic controller cut out fireplace.Self-operated thermostatic controller fireplace system roughly remains on fixed value with indoor temperature, and no matter the external disturbance such as outdoor temperature descends.In many application, use similar FEEDBACK CONTROL.

The primary clustering of feedback control system is a controll plant, may be defined as a machine or a process of " equipment ", and its output variable needs control.In above-mentioned example, " equipment " is dwelling house, and output variable is the indoor air temperature of premises, and interference is by the hot-fluid of dwelling house wall (propagation).Equipment is controlled by control system.In above example, control system is the combination of self-operated thermostatic controller and fireplace.Self-operated thermostatic controller fireplace system uses simple switch feedback control system, to keep indoor temperature.In many controling environment such as drive of motor shaft position and motor speed control system, simple switch FEEDBACK CONTROL is not enough.More advanced control system relies on the combination of proportional feedback control, integral feedback control and Derivative Feedback control.The FEEDBACK CONTROL that adds the Derivative Feedback sum based on proportional-plus-integral is called PID control.

The PID control system is a kind of linear control system based on the equipment dynamic model.In classical control system,, obtain linear dynamic model with the form of dynamic equation (normally ordinary differential equation).Suppose that equipment is linear relatively, does not change in time, and is stable.Yet the many equipment in the real world change in time, and are highly nonlinear, and are unsettled.For example, dynamic model may comprise parameter (as quality, induction coefficient, aerodynamic characteristics coefficient etc.), can only know the approximate value of these parameters, and perhaps these parameters are decided with the environment of continuous variation.If parameter changes little and dynamic model is stable, then the PID controller may be suitable.Yet,, add self-adaptation or intelligence (AI) control function to the PID control system usually if parameter changes greatly and dynamic model is unsettled.

The AI control system is used an optimizer (normally nonlinear optimization device), with the operation of planning PID controller, thereby improves the integrated operation of control system.

Classical Advanced Control theory is based on following hypothesis, and mode that promptly can linear system is approached all controlled " equipment " of approximate equilibrium point.Unfortunately, this hypothesis is set up hardly in real world.Most equipment all is highly nonlinear, and does not possess simple control algolithm usually.In order to satisfy the demand of nonlinear Control, people have developed the system that uses the soft calculating notion such as genetic algorithm (GA), fuzzy neural network (FNN), fuzzy controller.Utilize these technology, control system in time develops (change), so that itself adapts to the variation that may occur in controlled " equipment " and/or the operating environment.

Fig. 1 represents the control system according to soft calculation control equipment.

By using one a group of input and an objective function (fitness), genetic algorithm works in the mode that is similar to evolutionary process, to reach the optimum solution of hope.

Genetic algorithm generates " chromosome " (being feasible solution) set, by using objective function to calculate the value of respectively separating, chromosome is sorted then.Objective function determines respectively to separate the grade for the target value scope.Relatively the chromosome of Shi Heing (separating) is separated grade high dyeing body on the target value scope for it.Not too the chromosome of Shi Heing (separating) is separated junior chromosome on the target value scope for it.

Preserve the chromosome (survival) that relatively is fit to, abandon the chromosome (death) that not too is fit to.Create the chromosome of new chromosome to replace abandoning.Creating new chromosomal method is, intersects to have chromosomal some section now, and introduces variation.

The PID controling appliance has linear transfer function, and therefore, the PID controller is based on the linear equation of the motion of controlled " equipment ".The genetic algorithm that is used to plan the prior art of PID controller is used simple fitness, therefore can not solve the relatively poor controllability problem of seeing usually in inearized model.As seeing in most of optimizer, the success of optimization or failure usually finally depend on performance (fitness) function of selection.

It is normally difficult to calculate the motion feature of non-linear equipment, and some reasons are to lack general analytical approach.By convention, when utilizing nonlinear motion feature opertaing device, common way is to search some equilibrium point of equipment, then near the motion feature of linearization equipment certain equilibrium point.Then, control according near the puppet of equilibrium point, calculating (linearizing) motion feature.For utilizing unstable or dispersing for the equipment of model description, above technology almost (perhaps basic) is invalid.

Calculate optimum control according to soft calculating and comprise GA, GA is the first step of global search optimum solution on the fixed space of normal solution.GA searches for one group of control weight of this equipment.At first, conventional proportion integration differentiation (PID) is used weight vectors K={k ₁..., k _nGenerate the signal δ (k) be applied to this equipment.Suppose that the entropy S (δ (k)) relevant with the running of equipment on this signal is for wanting minimized objective function.With Fixed Time Interval GA is repeated several times, to generate one group of weight vectors.The vector that GA is generated offers FNN then, and the output of FNN is offered fuzzy controller.Fuzzy controller is output as the set of gain program of the PID controller of opertaing device.For for the soft computing system of GA, there is not the working control law on the classical control Significance usually, on the contrary, control is based on physics control law such as minimum entropy.

Obtain the more control of robust like this, its reason is to have guaranteed robustness with the GA that feeds back combination.Yet robust control may not be optimum control.GA attempts to search the globally optimal solution of given solution space.Any random disturbance of equipment (m among Fig. 1 (t)) all might " be played GA " in the different solution spaces.

Ideal situation is to search for globally optimal solution in many solution spaces, to search " general " optimum solution.

The new control algolithm based on knowledge of (as in controlling object) application in the high-grade intelligent control theory of complex dynamic systems must the new disposal route of exploitation such as computational intelligence (CI).The traditional calculations master tool that is used for CI is GA, FNN, fuzzy set theory, evolution program design, qualitative probabilistic reasoning etc.In the Advanced Control theory of complication system motion, use CI two kinds of research modes are arranged: 1) the stable non-equilibrium motion of research complex dynamic systems; With 2) research complex dynamic systems unsettled non-equilibrium motion.

In first kind of situation (stable non-equilibrium motion), can utilize the exploitation and the design of structrual description intelligent control algorithm shown in Figure 1.

Be for the characteristic of fixed structure, consider controlling object according to "black box" or the fuzzy system theory the nonlinear model such as equipment.Research of " input and output " relation and optimization are based on soft calculating, as GA, FNN and fuzzy control (FC), describe the Changing Pattern of PID controller parameter to utilize minimum entropy value and departure.In little original state at random, for the uncontrollable external drive or the minor alteration of the parameter or the structure of controll plant (equipment), but the method guarantees robust, the stable control of fixed space that row energization is conciliate.

In the unsettled dynamic controlled target situation of the overall situation, this based on existing robust, the stable method of controlling to guarantee success usually.For this type of unsettled dynamic controlled target, be necessary according to the understanding of nonlinear, unsettled, incomplete dynamic system motion in essence, develop a kind of new intelligence, the robust algorithm.

Summary of the invention

The objective of the invention is to,, provide the new method of control general process and the architecture of relevant hardware by the algorithm that uses merging genetic algorithm and quantum search algorithm to obtain.

The hardware configuration of the general control systems of its number of sensors minimizing has been described.Several actual embodiment of this class formation has been described.For example, the brand new of the application of the invention, the control system that the number of sensors of realization internal combustion engine and vehicle suspension system reduces.

In essence, method of the present invention and hardware configuration also can be used for the data of search database or similar application.

The integrated silicon equipment of the circuit of the different step that comprises the method that realizes the present invention has been described simultaneously.

The appended claims letters are bright to have defined the present invention.

Description of drawings

By the reference accompanying drawing, read the explanation of following several important embodiments, characteristic of the present invention and advantage will be clearer, and wherein accompanying drawing is:

Fig. 1 is based on the general structure of the intelligence control system of soft calculating;

Fig. 2 is based on the general structure of the intelligent dexterous control system of quantum soft calculating;

Fig. 3 is the block diagram of quantum algorithm;

Fig. 4 is the block diagram of scrambler;

Fig. 5 is the general structure of quantum piece among Fig. 3;

Fig. 6 is the example of quantum circuit;

Fig. 7 .a represents the example of tensor product conversion;

Fig. 7 .b represents the example of a product transformation;

Fig. 7 .c represents identical transformation;

Fig. 7 .d represents the example of propagation rule;

Fig. 7 .e represents the example of rule of iteration;

Fig. 7 .f explains I/O tensor rule;

Fig. 8 is for realizing the practical circuit of Grover quantum door (logic gate);

Fig. 9 is a Grover quantum door;

Figure 10 .a represents one group of possible input probability amplitude;

Figure 10 .b represents one group of probability amplitude after the step 1 shown in Figure 8;

Figure 10 .c represents one group of probability amplitude after the step 2 shown in Figure 8;

Figure 10 .d represents one group of probability amplitude after the step 3 shown in Figure 8;

Figure 11 .a is a vector stack example;

Figure 11 .b is for using ⁴Vector set among Figure 11 .a after the H;

Figure 11 .c is for using braiding operator U _F(x=001) vector set among Figure 11 .b afterwards;

Figure 11 .d is application of interference operator D _nVector set among Figure 11 .b after the  I;

Figure 11 .e is for using braiding operator U once more _FVector set among Figure 11 .b afterwards;

Figure 11 .f is application of interference operator D once more _nVector set among Figure 11 .b after the  I;

The compress information analysis of Grover algorithm of general iterations of Figure 11 .g (table 1);

The compress information analysis of Grover algorithm of first iteration of Figure 11 .h (table 2);

The compress information analysis of Grover algorithm of secondary iteration of Figure 11 .i (table 3);

Figure 12 represents the similarity between GA and the QSA;

Figure 13 is the block diagram of QGSA;

Figure 14 is the block diagram of quantum genetic searching algorithm;

Figure 15 describes and is used for the classical genetic search algorithm of global optimization and the structure of quantum search algorithm;

Figure 16 describes the general structure of quantum algorithm;

Figure 17 describes the quantum network of quantum search algorithm;

Figure 18 represents quantum search algorithm;

Figure 19 represents several possible flight distribution figure situations;

Figure 20 .a is the different dynamic characteristic at the pitch angle of fuzzy control simulation back vehicle relatively;

The phase graph of the time diagram of Figure 20 .b comparison diagram 20.a;

The entropy accumulation of the corresponding kinematic behavior shown in Figure 21 .a comparison diagram 20.a;

The phase graph of the time diagram of Figure 21 .b comparison diagram 21.a;

Figure 22 is the block diagram of accelerator of the present invention;

Figure 23 is the block diagram of the quantum door of realization Grover algorithm;

Figure 24 is the example that is used for the quantum door of Deutsch-Jozsa algorithm;

Figure 25 is the embodiment of the stack subsystem of Deutsch-Jozsa algorithm;

Figure 26 is the embodiment of the interference avoidance subsystem of Deutsch-Jozsa algorithm;

Figure 27 is the example that is used for the quantum door of Grover algorithm;

Figure 28 is the embodiment of the stack subsystem of Grover algorithm;

Figure 29 is the embodiment of the interference avoidance subsystem of Grover algorithm;

Figure 30 is the embodiment of K braiding subsystem;

Figure 31 is the embodiment of K interference avoidance subsystem;

Figure 32 is the foundation structure of the intelligence control system simulator of its number of sensors minimizing;

Figure 33 a is the detailed structure of the intelligence control system simulator that reduces of its number of sensors shown in Figure 32;

The compress implication of the table shown in Figure 33 a of Figure 33 b (table 4);

Figure 34 describes piston IC engine;

Figure 35 is the block diagram of simplified control system of internal combustion engine of quantum genetic searching algorithm of being unrealized;

Figure 36 is the block diagram of the simplified control system of the internal combustion engine of realization quantum genetic searching algorithm.

Embodiment

As mentioned above, intuitively it seems, basic sides of the present invention is, by merging the algorithm that quantum algorithm and genetic algorithm obtain being called the quantum genetic searching algorithm, to (prove in fact, already) and greatly strengthen the function that church's fuzzy neural network realizes the data in intelligence control system and the search database.

Above-mentioned merging is feasible, and its reason is " similarity " between quantum algorithm and the genetic algorithm, and for the description of easy to understand the present invention's brand-new quantum genetic searching algorithm, brief overview Genetic Algorithms Theory and quantum algorithm theory are of great use.

Genetic algorithm

Genetic algorithm (GA) is based on the global search algorithm of nature heredity and natural selection mechanism.In genetic search, the binary string of finite length is represented each design variable, with the collective encoding of all feasible solutions in the population of binary string.Subsequently, use and biological self reproducing and the similar hereditary conversion of evolving change and then improve separating through coding.Usually, three main operators using in genetic search are: intersect, make a variation and select.

Select processing to make search in population, generate the member who is more suitable for, and the not too suitable member of deletion.Therefore, at first each string in the population is distributed an adaptive value.Selecting member's straightforward procedure from initial population is based on its adaptive value, to distribute the probability of selecting this member for each member.Create then and have higher average adaptive value and its size new population identical with initial population.

Select to handle the more copies that only cause the dominance design that will in population, occur.Cross processing allows the design characteristics between the member in the exchange population, to improve follow-on adaptability.Cross processing refers to select father's string of two pairings, selects two positions on the string at random, exchanges 0 between the selected location, 1 string then.

Variation protection genetic search is handled in selection with during intersecting and can not lost valuable hereditary information too early.Variation is handled and to be, based on its variation probability, selects the minority member from population, then with the aberration rate of selecting at random of selected string, becomes 0 with 1, or on the contrary.

In above-mentioned argumentation, the mechanism of genetic search is simple.Yet the classic method that influences the intensity of this method has some key difference.GA only handles function evaluation, does not need functional derivative.And the derivative influence converges to optimum solution quickly, also may make search towards locally optimal solution.In addition, because the several points of search from the design space proceed to another group design point, so with respect to other patterns that proceed to another point from certain point, the possibility of this method location global minimum is higher.In addition, the coding of genetic algorithm Treatment Design variable rather than treatment variable itself.This permission expands to this algorithm by continuous, discrete and integer variable and mixes in the design space of forming.

In the GA environment that binary string is handled, pattern (being the similarity template) for from alphabet 0,1, the symbol string of choosing among the #}.Character # represents " haveing nothing to do " symbol, and therefore, a pattern can be represented the character string of several bits.For example, pattern #10#1 represents four character strings: 10011,01011,11001 and 11011.The number of non-# symbol is called the rank O (H) of pattern H.Distance between two non-# symbols farthest is called the definition length L (H) of this pattern.

Holland obtains following result (pattern theorem), and the character string number in the population of this theorem prediction and certain pattern match (belonging to certain pattern) is from a generation to follow-on situation of change (Holland, 1992).This theorem is:

Wherein m (H, t) be in t generation with H characters matched string number, (H t) is and the mean fitness of H characters matched string that f (t) is the mean fitness of character string in this population, p to f _mBe every variation probability, p _cBe crossover probability, N is the figure place in this character string, and M is a character string number in this population, E[m (H, t+1)] be in t+1 generation with the expectation number of pattern H characters matched string.This formula has a shade of difference with the original theorem of Holland.When choosing parent simultaneously from the mating pond and intersect, formula (1) is suitable for (Goldberg, 1989).Three horizontal braces below the equation represent which operator is responsible for this.Bracket above the equation is illustrated in t generation the Probability p of failure mode H owing to intersect _d(H, t).This probability depends on the frequency of this pattern in the mating pond, and the intrinsic fragility L (H)/(N-1) of this pattern.

Quantum algorithm

The problem that quantum algorithm solves can be stated as:

Input	Function f: 0,1} n→{0，1} m
		Problem	Search certain attribute of f

Utilize the structure of the senior expression summary description quantum algorithm in the synoptic diagram shown in Figure 3.

The input of quantum algorithm is the function f from the binary string to the binary string always.With this function representation is a mapping table, and the latter defines the map of each string.At first function f is encoded to the unit matrix operator U that relies on the f attribute _FOn some meaning, when the input and output string encoding with this function was the standard base vector in plural Hilbert space, this operator calculated f:U _FUtilize f the vector coding of each string to be mapped as the vector coding of its map.

Square frame 1: unit matrix U FSquare matrix U on the complex field FBe unit matrix, if its inverse matrix conforms to its conjugate transpose: U F -1=U FUnit matrix is always reversible, and keeps the norm of vector.

As generator matrix operator U _FThe time, it is embedded into The quantum doorAmong the G, G is that its structure depends on matrix U _FNorm and the unit matrix of the problem that we need solve.The quantum door is the core of quantum algorithm.In each quantum algorithm, the quantum gate action (is called so that generate the complex linear combination of base vector in initial standard base vector (we can always select identical vector) Stack) as output.More than stack comprises all information of the original problem that will answer.

After creating stack, carry out MeasureTo extract above information.In quantum mechanical, measurement is a uncertain operation, and this operation generates a base vector that enters stack as output.As the probability of each base vector of the output of measuring depend on the plural coefficient that enters in the complex linear combination ( Probability Amplitude).

The part operation structure of quantum door and measurement Become the quantum pieceThe quantum piece is repeated k time, so that generate the set of a k base vector.Because measuring is a uncertain operation, so these base vectors needn't equate that and each base vector will need a segment information of the problem that solves to encode.

The decline of this algorithm is, explains the base vector of collecting, so that obtain the correct answer of original problem with certain probability.

Scrambler

Synoptic diagram among Fig. 4 describes the characteristic of coder block in detail.

With three steps function f is encoded to matrix U _F

Step 1

With function f: 0,1} ⁿ→ 0,1} ^mMapping table be transformed to InjectionFunction F: 0,1} ^N+m→ 0,1} ^N+mMapping table so that:

F(x ₀，..，x _n-1，y ₀，..，y _m-1)?＝(x ₀，..，x _n-1，f(x ₀，..，x _n-1)(y ₀，..，y _m-1)) (2)

The reason that needs to handle injective function is to require U _FIt is unit matrix.Unit operator is reversible, so 2 different inputs can not be mapped as same output.Because U _FBe the matrix representation of F, so hypothesis F is injection.If the matrix representation of we direct utility function f may obtain a non-unit matrix, its reason is that f may not be injection.Therefore, by increasing figure place and considering that function F (rather than function f) realizes injectivity.In any case, by with (y ₀..., y _M-1)=(0 ..., 0) place input string, and read back m value of output string, always can from F, calculate function f.

Square frame 2:XOR operator length is that two the binary string p of m and the XOR operator between the q are that length is the binary string s of m, wherein calculates the i bit digital of s in the mutual exclusion OR mode between the i bit digital of p and q: p=(p 0，...，p n-1) q＝(q 0，...，q n-1) s＝pq＝((p 0+q 0)mod?2，...，(p n-1+q n+1)mod?2)

Step 2

The function F mapping table is transformed to U _FMapping table, satisfy following constraint:

s∈{0，1} ^n+m：U _F[τ(s)]＝τ[F(s)] (3)

Coding mapping τ: 0,1} ^N+m→ C ^{2 (n+m)}(C ^{2 (n+m)}Be target plural number Hilbert space) be:

$\left(0\right)=\left(\begin{array}{c}1\\ 0\end{array}\right)=|0\⟩,\mathrm{\τ}\left(1\right)=\left(\begin{array}{c}0\\ 1\end{array}\right)=|1\⟩$

τ(x ₀，..，x _n+m-1)＝τ(x ₀)..τ(x _n+m-1)＝|x ₀..x _n+m-1>

Coding τ is mapped to place value and belongs to C ²Standard base two-dimentional complex vector located.In addition, by using tensor product, τ is mapped as one 2 with the general state that n ties up binary string ⁿThe vector of dimension, thus this state is reduced to the united state of the n position that constitutes register.With each state transformation is corresponding 2 dimension base vectors, by utilizing tensor product to constitute all bit vectors, the character string state is mapped to corresponding 2 then ⁿThe dimension base vector.On this meaning, tensor product is the vectorial copy of state logic multiplication.

Example: vectorial tensor product

Use right (ket) mark of vowing | i〉the expression base vector.This mark is taken from quantum-mechanical Dirac and is described.

Step 3

Use following transformation rule with U _FMapping table is transformed to U _F:

[U _F] _ij＝1U _F|j>＝|i> (4)

By with vector | i〉and | j〉regard column vector as, can understand above rule easily.Because these vectors belong to the standard base, so U _FEach row of definition unit matrix The displacement mappingGenerally speaking, will go | j〉be mapped as row | i 〉.

Rule more than will in the first example-Grover algorithm of quantum algorithm, describing in detail.

The quantum piece

The core of quantum piece is The quantum door, the latter depends on matrix U _FAttribute.Fig. 5 is the detailed description of quantum piece.

Matrix operator U among Fig. 5 _FOutput for coder block shown in Figure 4.Here, it becomes the input of quantum piece.

At first this matrix operator is embedded into a more complicated door: quantum door G.It is 2 that unit matrix G is applied to dimension ^N+mThe initial specifications base vector | i 〉, k time altogether.Each consequent plural number stack G|0..01..1 that all measures base vector 〉, thus a base vector generated | x _iAs a result of.Collect in the lump all measurements base vector | x ₁..., | x _k.This set is the output of quantum piece.

" intelligence " of this type of algorithm is to create the quantum door, and the quantum door can extract the essential required information of attribute of searching f, and is stored in the output vector set.

Below discuss in detail the structure of the quantum door of each quantum algorithm, notice that general description gets final product.

In order to represent the quantum door, we will use some to be called Quantum circuitSpecial chart.

Fig. 6 represents the example of quantum circuit.Each rectangle all with one 2 ⁿ* 2 ⁿThe matrix association, wherein n is the number of lines that enters and leave this rectangle.For example, be labeled as U _FRectangle and matrix U _FRelated.

Quantum circuit makes us can give the senior description of going out, and by using some transformation rule shown in Figure 7, can be corresponding gate matrix with these rule encodings.

By first example of quantum algorithm is provided, these regular use-patterns will be understood more.

Example: matrix tensor product

Code translator

The function of decoder block is to explain in iteration to carry out the base vector of collecting behind the quantum piece.These vectors are deciphered meaning remaps them is binary string,, then directly explain them, perhaps, separate so that obtain search for example with they coefficient vectors as some system of equations if they have comprised the answer of primal problem.Because this part is our uninterested, understandable classical part, so do not study this part in great detail.

Because the Grover algorithm is for the realization particular importance of controller, so simple declaration Grover algorithm.

The Grover problem

The Grover problem is:

In the Deutsch-Jozsa algorithm, we distinguish two class input functions, and we must determine which kind of input function belongs to.At this moment, this problem is identical with its form in some sense, just because we will handle 2 ⁿThe input function of class (every kind of function of description constitutes a class) is so this problem more is difficult to handle.

Scrambler

In order to make the discussion easy to understand, at first consider the special function of n=2.The generalized case of n=2 then is discussed, the generalized case of ultimate analysis n＞0.

A1. introductory example

Consider following situation:

n＝2 f(01)＝1

In above situation, the f mapping table is defined as:

?x	?f(x)
		?00	?0
?01	?1
		?10	?0
?11	?0

Step 1

According to following formula function f is encoded to injective function F:

F:{0,1} ^N+1→ 0,1} ^N+1: F (x ₀, x ₁, y ₀)=(x ₀, x ₁, f (x ₀, x ₁) y ₀) therefore, the F mapping table is:

(x 0，x 1，y 0)	?F(x 0，x 1，y 0)
		000	000
010	011
		100	100
110	110
		001	001
011	010
		101	101
111	111

Step 2

By using general rule that F is encoded to U _FMapping table:

s∈{0，1} ⁿ⁺¹：U _F[τ(s)]＝τ[F(s)]

Wherein, τ is the coding mapping of definition in the equation (3).This means:

|x 0?x 1?y 0>	?U F|x 0?x 1?y 0>
		|000>	|000>
|010>	|011>
		|100>	|100>
|110>	|110>
		|001>	|001>
|011>	|011>
		|101>	|101>
|111>	|111>

Step 3

We must be according to U _FMapping table calculate corresponding matrix operator.

By using following rule to obtain this matrix according to equation (4):

[U _F] _ij＝1U _F|j>＝|i>

Thereby obtain U _F:

?U F	|00>?|01> |10> |11>
		?|00> ?|01> ?|10> ?|11>	I 0 0 0 0 C 0 0 0 0 I 0 0 0 0 I

The result of this matrix is that to keep the first and second input base vectors of input tensor product constant, thereby when primary vector is | 0 and secondary vector be | 1〉time, reverse (flip) the 3rd vector.This and the U that narrates above _FThe constraint unanimity.

The generalized case of B.n=2

Consider more generally situation now:

n＝2 f( x)＝1

Corresponding matrix operator is:

U F	00>	01>	10>	11>
					00>	M 00	0	0	0
01>	0	M 01	0	0
					10>	0	0	M 10	0
11>	0	0	0	M 11

M wherein _x =C  i ≠ x: M _i=I.

C. generalized case

With operator U _FBe generalized to n＞1st from n=2, very natural.In fact, we are always corresponding to vector | xThe unit of mark, operator C on the principal diagonal of block matrix, searched, wherein xFor having the binary string of f map.Therefore:

?U F	|00>	|01>	…	|11>
					?|00>	M 00	0	…	0
?|01>	0	M 01	…	0
					?…	…	…	…	…
?|11>	0	0	…	M 11

M wherein _x =C  i ≠ x: M _i=I.

Matrix U with scrambler output _FBe embedded in the quantum door.We use all quantum circuits as shown in Figure 8 to describe the quantum door.

Operator D _nBe called the n rank Diffusion matrix, it is responsible for the interference in this algorithm.QFT in its effect and the Shor algorithm _nIdentical, and in Deutsch-Jozsa and Simon algorithm, have ⁿH.The definition mode of this matrix is:

D n	|0..0> |0..1> ... |i> ... |1..0> |1..1>
		|0..0> |0..1> |i> ... |1..0> |1..1>	-1+1/2 n-1 1/2 n-1 ... 1/2 n-1 ... 1/2 n-1 1/2 n-1 1/2 n-1 -1+1/2 n-1 ... 1/2 n-1 ... 1/2 n-1 1/2 n-1 1/2 n-1 1/2 n-1 -1+1/2 n-1 ... 1/2 n-1 1/2 n-1 ... ... ... ... ... ... ... 1/2 n-1 1/2 n-1 ... 1/2 n-1 ... -1+1/2 n-1 1/2 n-1 1/2 n-1 1/2 n-1 ... 1/2 n-1 ... 1/2 n-1 -1+1/2 n-1

By using identical transformation (Fig. 7 .c), can with former circuit code the circuit of Fig. 9.

A2. introductory example: performance analysis

In the introductory example that we handle, U _FHave following form:

?U F	|00> |01> |10> |11>
		?|00> ?|01> ?|10> ?|11>	I 0 0 0 0 C 0 0 0 0 I 0 0 0 0 I

We calculate the quantum door G=[(D in the above-mentioned situation ₂ I) U _F] ^h( ²⁺¹H):

? 3H	|00> |01> |10> |11>
		?|00> ?|01> ?|10> ?|11>	H/2 H/2 H/2 H/2 H/2 -H/2 H/2 -H/2 H/2 H/2 -H/2 -H/2 H/2 -H/2 -H/2 H/2

D 2I	|00> |01> |10> |11>
		|00> |01> |10> |11>	-I/2 I/2 I/2 I/2 I/2 -I/2 I/2 I/2 I/2 I/2 -I/2 I/2 I/2 I/2 I/2 -I/2

U F· 3H	|00> |01> |10> |11>
		|00> |01> |10> |11>	H/2 H/2 H/2 H/2 CH/2 -CH/2 CH/2 -CH/2 H/2 H/2 -H/2 -H/2 H/2 -H/2 -H/2 H/2

Select h=1, obtain:

G	|00> |01> |10> |11>
		|00> |01> |10> |11>	(C+I)H/4 (-C-I)H/4 (C-3I)H/4 (-C-I)H/4 (-C+3I)H/4 (C+I)H/4 (-C-I)H/4 (C+I)H/4 (C+I)H/4 (-C-I)H/4 (C+I)H/4 (-C+3I)H/4 (C+I)H/4 (-C+3I)H/4 (C+I)H/4 (-C-I)H/4

Now, consider G is applied to vector | 001 〉:

$\begin{array}{c}G|001\⟩=\frac{1}{4}|00\⟩\⊗(C+I)H|1\⟩+\frac{1}{4}|01\⟩\⊗(-C+3I)H|1\⟩+\\ \frac{1}{4}|10\⟩\⊗(C+I)H|1\⟩+\frac{1}{4}|11\⟩\⊗(C+I)H|1\⟩\end{array}$

Calculate operator (C+3I) H/4.

-C+3I	|0> |1>
		|0> |1>	3 -1 -1 3

(-C+3I)H/4	|0> |1>
		|0> |1>	1/23/2 1/21/2 1/23/2 -1/21/2

Therefore:

$\frac{1}{4}(-D+3I)H|1\⟩=\frac{1}{\sqrt{2}}\left(\right|0\⟩-|1\⟩)$

Calculate operator (C+I) H/4.

C+I	?|0> |1>
		|0> |1>	?1 1 ?1 1

(C+I)H/4	0> 1>
		0> 1>	1/23/2 0 1/23/2 0

Therefore:

$\frac{1}{4}(C+I)H|1\⟩=0$

This means will | 001〉be mapped to vector | 01〉(| 0 〉-| 1 〉)/2 ^1/2By the record dimension is the binary value of preceding two vectors of 2, obtains x

Describe order and use operator ³H, U _FAnd D ₂Perhaps the differentiation of the probability amplitude of each base vector is useful during  I.Figure 10 represents the differentiation of probability amplitude.

Operator ³H is with initial standard base vector | 001 become the stack (modular arithmetic) of all base vectors and same (reality) coefficient, if but the end vector be | 0 〉, then be positive sign, otherwise be negative sign.Operator U _FCreate Relevant: if preceding two vectors are | 0〉and | 1 〉, then reverse the 3rd vector.At last, D ₂ I produces Disturb: for each base vector | x ₀ x ₁ y ₀, it calculate each vectorial output probability amplitude alpha ' _X0x1y0, its method is that its initial probability amplitude α reverses _X0x1y0, add up | x ₀x ₁ y ₀The mean value of probability amplitude of institute's directed quantity of form α _Y0Twice.In our example, α ₀=1/ (42 ^1/2), α ₁=-1/ (42 ^1/2).For example, get base vector | 000 〉.α ' then ₀₀₀=-α ₀₀₀+ 2 α ₀=-1/ (22 ^1/2)+2/ (42 ^1/2)=0.

The generalized case of D.n=2

Generally speaking, if n=2, then U _FHave following form:

?U F	|00>	|01>	|10>	|11>
					?|00>	M 00	0	0	0
?|01>	0	M 01	0	0
					?|10>	0	0	M 10	0
?|11>	0	0	0	M 11

M wherein _x =C  i ≠ x: M _i=I ( x, i ∈: 0,1} ⁿ).

We calculate the quantum door G=(D in the generalized case ₂ I) U _F( ²⁺¹H):

U F· 3H	|00> |01> |10> |11>
		|00> |01> |10> |11>	M 00H/2 M 00H/2 M 00H/2 M 00H/2 M 01H/2 -M 01H/2 M 01H/2 -M 01H/2 M 10H/2 M 10H/2 -M 10H/2 -M 10H/2 M 11H/2 -M 11H/2 -M 11H/2 M 11H/2

?G	|00> |01>
		?|00> ?|01> ?|10> ?|11>	(-M 00+M 01+M 10+M 11)H/4 (-M 00-M 01+M 10-M 11)H/4 (M 00-M 01+M 10+M 11)H/4 (M 00+M 01+M 10-M 11)H/4 (M 00+M 01-M 10+M 11)H/4 (M 00-M 01-M 10-M 11)H/4 (M 00+M 01+M 10-M 11)H/4 (M 00-M 01+M 10+M 11)H/4

?G	|10> |11>
		?|00> ?|01> ?|10> ?|11>	(-M 00+M 01-M 10-M 11)H/4 (-M 00-M 01-M 10+M 11)H/4 (M 00-M 01-M 10-M 11)H/4 (M 00+M 01-M 10+M 11)H/4 (M 00+M 01+M 10-M 11)H/4 (M 00-M 01+M 10+M 11)H/4 (M 00+M 01-M 10+M 11)H/4 (M 00-M 01-M 10-M 11)H/4

Now, consider G is applied to vector | 001 〉:

$\begin{array}{c}G|001\&rang;=\frac{1}{4}|00\&rang;\&CircleTimes;(-{\mathrm{<figure-callout\; id="00"\; label="M"\; filenames="A200510082346.100731.png"\; state="\{\{state\}\}">M</figure-callout>}}_{00}+{\mathrm{<figure-callout\; id="01"\; label="M"\; filenames="A200510082346.100621.png"\; state="\{\{state\}\}">M</figure-callout>}}_{01}+{\mathrm{<figure-callout\; id="10"\; label="M"\; filenames="A200510082346.100621.png,A200510082346.100671.png"\; state="\{\{state\}\}">M</figure-callout>}}_{10}+M_{11})H|1\&rang;+\frac{1}{4}|01\&rang;\&CircleTimes;(M_{00}-{\mathrm{<figure-callout\; id="01"\; label="M"\; filenames="A200510082346.100621.png"\; state="\{\{state\}\}">M</figure-callout>}}_{01}+{\mathrm{<figure-callout\; id="10"\; label="M"\; filenames="A200510082346.100621.png,A200510082346.100671.png"\; state="\{\{state\}\}">M</figure-callout>}}_{10}+M_{11})H|1\&rang;+\\ \frac{1}{4}|10\&rang;\&CircleTimes;({\mathrm{<figure-callout\; id="00"\; label="M"\; filenames="A200510082346.100731.png"\; state="\{\{state\}\}">M</figure-callout>}}_{00}+M_{01}-{\mathrm{<figure-callout\; id="10"\; label="M"\; filenames="A200510082346.100621.png,A200510082346.100671.png"\; state="\{\{state\}\}">M</figure-callout>}}_{10}+M_{11})H|1\&rang;+\frac{1}{4}|11\&rang;\&CircleTimes;({\mathrm{<figure-callout\; id="00"\; label="M"\; filenames="A200510082346.100731.png"\; state="\{\{state\}\}">M</figure-callout>}}_{00}+{\mathrm{<figure-callout\; id="01"\; label="M"\; filenames="A200510082346.100621.png"\; state="\{\{state\}\}">M</figure-callout>}}_{01}+M_{10}-M_{11})H|1\&rang;\end{array}$

Consider following situation:

x＝00：

$\begin{array}{c}G|001\&rang;=\frac{1}{4}|00\&rang;\&CircleTimes;(-C+3I)H|1\&rang;+\frac{1}{4}|01\&rang;\&CircleTimes;(C+I)H|1\&rang;+\\ \frac{1}{4}|10\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|11\&rang;\&CircleTimes;(C+I)H|1\&rang;=|00\&rang;\left(\frac{|0\&rang;-|1\&rang;}{\sqrt{2}}\right)\end{array}$

x＝01：

$\begin{array}{c}G|001\&rang;=\frac{1}{4}|00\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|01\&rang;\&CircleTimes;(-C+3I)H|1\&rang;+\\ \frac{1}{4}|10\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|11\&rang;\&CircleTimes;(C+I)H|1\&rang;=|01\&rang;\left(\frac{|0\&rang;-|1\&rang;}{\sqrt{2}}\right)\end{array}$

x＝10：

$\begin{array}{c}G|001\&rang;=\frac{1}{4}|00\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|01\&rang;\&CircleTimes;(C+I)H|1\&rang;+\\ \frac{1}{4}|10\&rang;\&CircleTimes;(-C+3I)H|1\&rang;+\frac{1}{4}|11\&rang;\&CircleTimes;(C+I)H|1\&rang;=|10\&rang;\left(\frac{|0\&rang;-|1\&rang;}{\sqrt{2}}\right)\end{array}$

x＝11：

$\begin{array}{c}G|001\&rang;=\frac{1}{4}|00\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|01\&rang;\&CircleTimes;(C+I)H|1\&rang;+\\ \frac{1}{4}|10\&rang;\&CircleTimes;(C+I)H|1\&rang;+\frac{1}{4}|11\&rang;\&CircleTimes;(-C+3I)H|1\&rang;=|11\&rang;\left(\frac{|0\&rang;-|1\&rang;}{\sqrt{2}}\right)\end{array}$

This means that if we measure output vector dimension is preceding two base vectors of 2 in the consequent tensor product of phase-reversal coding then, thereby obtains following result:

x	The result	Probability
				00	?00	?1
01	?01	?1
			10	?10	?1
11	?11	?1

E. generalized case (n＞0)

In the generalized case of n＞0, U _FHave following form:

?U F	|0..0＞ |0..1＞... |1..1＞

?|0..0>	M 0..0	0	0	?0
					?|0..1>	0	M 0..1	0	?0
?...	...	...	...	?...
					?|1..1>	0	0	?0	?M 1..1

M wherein _x =C  i ≠ x: M _i=I ( x, i ∈: 0,1} ⁿ).

Calculated amount cervical orifice of uterus G=(D _n I) ^hU _F( ^N+1H):

n+1H	?|0..0> ... |j> ... |1..1>
		|0..0> ... |i> ... |11>	?H/2 n/2 ... H/2 n/2 ... H/2 n/2?... ... ... ... ... ?H/2 n/2 ... (-1) i·jH/2 n/2 ... (-1) i·(1..1)H/2 n/2?... ... ... ... ... ?H/2 n/2 ... (-1) (1..1)·jH/2 n/2 ... (-1) (1..1) ·(1..1)H/2 n/2

D nI	|0..0> |0..1> ... |i> ... |1..0> |1..1>
		|0..0> |0..1> ... |i> ... |1..0> |1..1>	-I+I/2 n-1 I/2 n-1 ... I/2 n-1 ... I/2 n-1 I/2 n-1I/2 n-1 -1+I/2 n-1 ... I/2 n-1 ... I/2 n-1 I/2 n-1... ... ... ... ... ... ... I/2 n-1 I/2 n-1 ... -I+I/2 n-1?... I/2 n-1 I/2 n-1... ... ... ... ... ... ... I/2 n-1 I/2 n-1 ... I/2 n-1 ... -I+I/2 n-1I/2 n-1I/2 n-1 I/2 n-1 ... I/2 n-1 ... I/2 n-1 -I+I/2 n-1

U F· n+1H	|0..0> ... |j> ... |1..1>
		|0..> ... |i> ... |1..1>	M 0..0H/2 n/2 ... M 0..0H/2 n/2 ... M 0..0H/2 n/2... ... ... ... ... M iH/2 n/2 ... (-1) i·jM iH/2 n/2 ... (-1) i·(1..1)M iH/2 n/2... ... ... ... ... M 1..1H/2 n/2 ... (-1) (1..1)·jM 1..1H/2 n/2 ... (-1) (1..1)·(1..1)M 1..1H/2 n/2

Now, suppose h=1.Then:

G h＝1	|0..0> ...
		|0..0>... |i>... |1..1>	(-M 0..0+∑ j∈{0，1}nM i/2 n-1)H/2 n/2 ... (-M i+∑ j∈{0，1}nM i/2 n-1)H/2 n/2 ... (-M 1..1+∑ j∈{0，1}nM i/2 n-1)H/2 n/2 ...

Because M _x =C and i ≠ x:M _i=I, so above each row can be written as:

G h＝1	|0..0> ...
		|0..0> ... | x> ... |1..1>	(-I+∑ j∈{0，1}n-{ x} I/2 n-1+C/2 n-1)H/2 n/2 ... ... ... (-C+∑ j∈{0，1}n-{ x} I/2 n-1+C/2 n-1)H/2 n/2 ... ... ... (-I+∑ j∈{0，1}n-{ x} I/2 n-1+C/2 n-1)H/2 n/2 ...

Therefore:

G h＝1	|0..0> ...
		|0..0> ... | x>? ... |1..1>	{[-1+(2 n-1)/2 n-1]I+C/2 n-1}H/2 n/2 ... ... ... {(2 n-1)/2 n-1I+[-1+1/2 n-1]C}H/2 n/2 ... ... ... {[-1+(2 n-1)/2 n-1]I+C/2 n-1}H/2 n/2 ...

Now, consider that { [1+ (2 with matrix operator ⁿ-1)/2 ^N-1] I+C/2 ^N-1H/2 ^N/2And matrix operator { (2 ⁿ-1)/2 ^N-1I+[-1+1/2 ^N-1] C}H/2 ^N/2Be applied to vector | 1 〉:

$\begin{array}{c}\frac{1}{2^{n/2}}\left\{\right[-1+\frac{2^n-1}{2^{n-1}}]I+\frac{1}{2^{n-1}}C\}H|1\&rang;=(-1+\frac{2^n-2}{2^{n-1}})\frac{|0\&rang;-|1\&rang;}{2^{\frac{(n+1)}{2}}}\\ \frac{1}{2^{n/2}}\{\frac{2^n-1}{2^{n-1}}I+[-1+\frac{1}{2^{n-1}}\left]C\right\}H|1\&rang;=(+1+\frac{2^n-2}{2^{n-1}})\frac{|0\&rang;-|1\&rang;}{2^{\frac{(n+1)}{2}}}\end{array}$

This means:

$\begin{array}{c}{G}_{h=1}|0..01\&rang;=[(-1+\frac{2^n-2}{2^{n-1}})|0..0\&rang;+(-1+\frac{2^n-2}{2^{n-1}})|0..1\&rang;+..+\\ +(+1+\frac{2^n-2}{2^{n-1}})|\underset{\&OverBar;}{x}\&rang;+..+(-1+\frac{2^n-2}{2^{n-1}})|1..1\&rang;]\&CircleTimes;\frac{|0\&rang;-|1\&rang;}{2^{\frac{(n+1)}{2}}}\end{array}$

Following formula can be written as the piece vector:

G h＝1|0..1>
		|0..0> ... | x> ... |1..1>	[-1+(2 n-2)/2 n-1]/2 n/2H|1> ... [+1+(2 n-2)/2 n-1]/2 n/2H|1> ... [-1+(2 n-2)/2 n-1]/2 n/2H|1>

Now, suppose to press Following form willOperator (D _n I) U _FBe applied to vector:

|>
		|0..0> ... |x> ... |1..1>	αH|1> ... βH|1> ... αH|1>

Wherein α and β are for satisfying (2 ⁿ-1) α ²+ β ²=1 real number.The result is:

U F·|>
		|0..0> ... | x> ... |1..1>	αH|1> ... βCH|1> ... αH|1>

(D nI)·U F·|>
		?|0..0> ?... ?| x> ?... ?|1..1>	(-α+∑ j∈{0，1}n-{ x} α/2 n-1-β/2 n-1)H|1> ... (+β+∑ j∈{0，1}n-{ x} α/2 n-1-β/2 n-1)H|1> ... (-α+∑ j∈{0，1)n-{ x} α/2 n-1-β/2 n-1)H|1>

(D nI)·U F·|>
		|0..0> ... | x> ... |1..1>	{-α+[(2 n-1)α-β]/2 n-1}H|1> ... {+β+[(2 n-1)α-β]/2 n-1}H|1> ... {-α+[(2 n-1)α-β]/2 n-1}H|1>

This means if we are from vectorial G _H=1| 0..01〉beginning, the form of this vector for considering, and use (D _n I) U _FOperator h time, then the coefficient of t satisfies constantly:

Therefore β increases, and α reduces.For example, consider that the vector among Figure 11 .a superposes.By using operator ⁴H, the stack of vector stack becoming Figure 11 .b.The braiding operator U that has x=001 by application _F, generate the vector stack of Figure 11 .c, using D _nAfter the  I, be superposed to the stack shown in Figure 11 .d.Here, although our probability amplitude of uninterested vector is non-vanishing, they are very little.

Suppose and use operator U once more _F: then Figure 11 .e represents consequent stack.Then, by using D _n I, we obtain the linear combination of the vector shown in Figure 11 .f.

Its modulus of probability amplitude that can see required vector increases.This means and can measure vector with big probability | 0010〉or | 0011 〉.

If repeating D _nU _FMeasure after operator h takes second place, then measure vector | x  | 0〉or | x〉 | 1〉probability P (h) what are? we can prove:

P’(h)＝O(2 ^-n/2)

As long as repeat quantum piece 1 time, just can obtain enough big h=O (2 ^N/2).Therefore, the final base vector of collecting is unique.

Information analysis

A3. introductory example: the information analysis of Grover algorithm

The operator that consideration is encoded to input function:

$U_F=\left[\begin{array}{cccccccc}I& 0& 0& 0& 0& 0& 0& 0\\ 0& \mathrm{<figure-callout\; id="0"\; label="C"\; filenames="A200510082346.100641.png,A200510082346.100661.png"\; state="\{\{state\}\}">C</figure-callout>}& 0& 0& 0& 0& 0& 0\\ 0& 0& I& 0& 0& 0& 0& 0\\ 0& 0& 0& I& 0& 0& 0& 0\\ 0& 0& 0& 0& I& 0& 0& 0\\ 0& 0& 0& 0& 0& I& 0& 0\\ 0& 0& 0& 0& 0& 0& I& 0\\ 0& 0& 0& 0& 0& 0& 0& I\end{array}\right]$

Table 1 expression is used for the general iterative algorithm of the information analysis of Grover QA.In table 2 and table 3, twice iteration of this algorithm described.From these tables, can see:

1. the braiding operator in each iteration increases the correlativity between the different quantum bits;

2. disturb operator to reduce classical entropy, but its spinoff is that it utilizes Feng's Neumann entropy to destroy part quantum correlativity and measures.

The built-in repeatedly iteration of Grover algorithm intellectual status (seeing equation (7)).Each iteration at first utilizes braiding that search function is encoded, but disturbs operator meeting partial destruction coded message; For hidden coded message and the needs visit coded message of needing, need iteration several times.The Grover algorithm is from the search groups of algorithm.Minimum classical (quantum) entropy principle in the output of QA means the successful result of relevant intelligent output state.Search QA need check the minimum value of classical entropy, and utilizes the quantum entropy to coordinate difference.Intelligent search QA is characterised in that and can coordinates above two values.

Code translator

As in the Deutsch algorithm, after the output vector of measuring amount cervical orifice of uterus, must explain that this vector is to search x

Find out that from above analysis this step is very simple.In fact, select a bigger h to be enough to obtain its probability near 1 search vector | x | 0〉or | x | 1 〉.After obtaining searching for vector, be its binary value with preceding n base vector reverse coding in the consequent tensor product, thereby obtain character string as final answer x

Therefore, show and in search problem, to use the Grover algorithm.

Search problem can be stated as: given truth-function f:{0,1} ⁿ→ 0,1} so that have only an input x ∈ 0,1} ⁿ: f (x)=1 searches x: the problem that this can utilize the Grover algorithm to solve just.

By the relatively above algorithm of analyzing, obvious quantum algorithm has same structure: one group of vector order is submitted to superposition operator, braiding operator and interference operator.Utilize the consequent vector set of the measurement block analysis of extracting information needed.

Have to be noted that at last that in essence the difference of different quantum algorithms is the interference operator Int that selects, braiding operator U _FWith superposition operator S.

Input vector is a message, and this message traversal is by three main subchannel-stacks, the quantum passage that weaves and disturb-form.The braiding passage is the true input of algorithm door.It belongs to certain given kind, this kind depend on the problem that will solve with and input.Superposeing particularly, the selection mode of interfering channel is: several measurements of carrying out at the passage end are disclosed in the woven type that channel middle takes place.

In a word, can be stated as, quantum algorithm is based on the global random searching algorithm of principle of quantum mechanics, law and quantum effect.In quantum searching, utilize each design variable of limited linear stack expression of classical original state, utilize the initial quantum state of a series of elementary cell step process | i〉(being used for input), so that correctly exported by the end-state of measuring system.It is at first from basic classical pre-service, uses following quantum experiment then: from institute might state initial stack, the calculating classical function, application quantum fast fourier transform (QFFT) is measured at last.Depend on the result, may carry out once similarly quantum experiment again, perhaps utilize some classical aftertreatment to finish calculating.Usually, quantum search algorithm uses three main operators, i.e. linear superposition (correlation behavior), braiding and interference.

The general type of the structure of quantum search algorithm can be described as:

Quantum algorithm and genetic algorithm structure have following mutual relationship:

Figure 12 compares the structure of GA and QSA.In GA, population generates at random in beginning.Use variation and crossover operator then, changing some individual genome, and create new genome.Delete some individuality according to objective function then, and select excellent individual to generate new population.New population is repeated said process, until finding optimum solution.

By analogy, in QSA, utilize superposition operator initial base vector to be transformed to the linear superposition of base vector.Then, quantum operators such as braiding and interference acts on above state stack, thereby generate new state, wherein the modulus of (uninterested state) its probability amplitude of some state reduces, and the probability amplitude of some state (most interested state) increases.With this process repeated several times, obtaining final probability amplitude, thereby can see optimum solution easily.

Quantum braiding operator class is similar to the hereditary variation operator: in fact, by reversing right some position of vowing in the mark, each base vector that this operator will enter stack is mapped as another base vector.The quantum interference operator class is similar to hereditary crossover operator, it from the interaction of the probability amplitude of the state that enters stack, the new stack of setting up basic state.But, disturb operator also to comprise the selection operator.In fact, disturb operator according to general principle, increase the probability amplitude modulus of some basic state, reduce the probability amplitude modulus of some basic state, general principle is for making this quantity maximum

T={1 wherein ..., n}.This quantity is called the intelligence of output state, and measures measuring method is handled the information that is encoded to the quantum correlativity to braiding the degree of understanding.In fact, the effect of disturbing operator is to keep to enter Feng's Neumann entropy of woven condition, and Shannon entropy is dropped to minimum value, and wherein superposition operator is increased to maximal value with Shannon entropy.The key distinction that note that GA and QSA is: in GA, objective function changes with the different instances of same problem, always and variation and intersecting at random.In QSA, (intelligence of output state) that objective function is always identical, and the braiding operator depends critically upon input function f.

In the present invention, we advise merging GA and the QSA pattern with similarity and integrated its characteristic.New model relates to quantum genetic searching algorithm (QGSA), and Figure 13 represents this pattern.

At first generate and have a t initial stack of nonzero probability amplitude at random

$|\mathrm{input}\&rang;=\underset{i=1}{\overset{i}{\mathrm{\&Sigma;}}}{c}_i|x_i\&rang;---\left(8\right)$

Each right arrow corresponding to the body one by one in the population, and in generalized case, use the real number mark.Therefore, each individuality is corresponding to a real number x _i, and utilize probability amplitude value c _iImplicit weighting.General simulation braiding and the operation of disturbing operator: select the different paths of k bar at random, wherein every paths is corresponding to using a braiding and disturbing operator.

The braiding operator is present in the injection mapping, and the latter is transformed to another base vector with each base vector.Its implementation is to define variation micro-ε＞0, and extract t different value ε ₁..., ε _iSatisfy-ε≤ε _i≤ ε.Then, utilize the braiding operator U of following transformation rule definition path j ^j _F:

$|x_i\&rang;\stackrel{U_F^j}{\&RightArrow;}|x_i+{\mathrm{\&epsiv;}}_i\&rang;---\left(9\right)$

Work as U ^j _FWhen acting on the initial linear stack, all base vectors in it make a variation

$|{\mathrm{\&psi;}}^j\&rang;=\underset{i=1}{\overset{i}{\mathrm{\&Sigma;}}}{c}_{i,j}|x_i+{\mathrm{\&epsiv;}}_{i,j}\&rang;---\left(10\right)$

Mutation operator ε can be described as following relation

8 kinds of states are arranged in the supposing the system, and its binary coding is 000,001,010,011,100,110,111.A kind of possibility state in the computation process be $\frac{i}{\sqrt{2}}|000\&rang;+\frac{1}{\sqrt{2}}|100\&rang;+\frac{1}{\sqrt{2}}|110\&rang;.$ Usually construct a unit transformation, so that carry out in bit-level.

For example, unit transformation

With state | 0〉become | 1 〉, will | 1〉become | 0〉(NOT operator).

In GA, chromosomal variation changes one or more genes.Also can describe by the position that changes some positions or certain several position.Only carry out single NOT conversion and also can change the position.

As an example, can utilize following matrix description, act on last two and with state | 1001〉become state | 1011〉and with state | 0111〉become state | 0101〉unit transformation

$\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\left(\begin{array}{cccc}\stackrel{00}{1}& \stackrel{01}{0}& \stackrel{10}{0}& \stackrel{11}{0}\\ 0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\end{array}\right)---\left(12\right)$

Be vector set | 0000, | 0001〉..., | 1111〉mutation operator.

Phase-shifts operator Z can be described as Z: $\begin{array}{c}|0\&rang;\&RightArrow;|0\&rang;\\ |1\&rang;\&RightArrow;-|1\&rang;\end{array}$ And operator $Y:\begin{array}{c}|0\&rang;\&RightArrow;|1\&rang;\\ |1\&rang;\&RightArrow;-|0\&rang;\end{array}$ It is the combination of NOT and phase-shifts operator Z.

Note 1.As an example, following matrix

$\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\left(\begin{array}{cccc}\stackrel{00}{1}& \stackrel{01}{0}& \stackrel{10}{0}& \stackrel{11}{0}\\ 0& 1& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\end{array}\right)---\left(13\right)$

Crossover operator is acted on last two, become 1010 and 0111 with 1011 and 0110, its point of interruption (a bit intersects) at the middle part.

Two condition phase-shifts doors have following matrix form

$\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\left(\begin{array}{cccc}\stackrel{00}{1}& \stackrel{01}{0}& \stackrel{10}{0}& \stackrel{11}{0}\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& e^{\mathrm{i\&phi;}}\end{array}\right)$

And utilize following matrix description can create controlled NOT (CNOT) door of woven condition:

$\mathrm{CNOT}:\begin{array}{c}|00\&rang;\&RightArrow;|00\&rang;\\ |01\&rang;\&RightArrow;|01\&rang;\\ |10\&rang;\&RightArrow;|11\&rang;\\ |11\&rang;\&RightArrow;|10\&rang;\end{array}\&DoubleRightArrow;\begin{array}{c}00\\ 01\\ 10\\ 11\end{array}\left(\begin{array}{cccc}\stackrel{00}{1}& \stackrel{01}{0}& \stackrel{10}{0}& \stackrel{11}{0}\\ 0& 1& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\end{array}\right)$

As rank is the positive square matrix of random units of t, selects to disturb operator Int ¹, wherein according to suitable law, according to Int ¹Generate the interference operator in other paths.The example of this matroid is Hadamard transformation matrix H defined above _tAnd diffusion matrix D _t, but also can construct other matrixes.Use braiding and disturb operator to generate the new stack that maximum length is t:

$|{\mathrm{output}}^j\&rang;=\underset{i=1}{\overset{i}{\mathrm{\&Sigma;}}}{c^{\&prime;}}_{i,j}|x_i+{\mathrm{\&epsiv;}}_{i,j}\&rang;---\left(14\right)$

Calculate the average entropy of this state now.Make E (x) be the entropy of individual x.Then

$E\left(\right|{\mathrm{output}}^j\&rang;)=\underset{i=1}{\overset{i}{\mathrm{\&Sigma;}}}{\left|\right|{c^{\&prime;}}_{i,j}\left|\right|}^{2}E(x_i+{\mathrm{\&epsiv;}}_{i,j})---\left(15\right)$

By squared absolute value with respect to probability amplitude, calculate the mean value of each entropy in this stack, calculate average entropy.

According to above sequence of operation,, generate the different stacks of k kind from initial stack by using different braidings and disturbing operator.All calculate average entropy at every turn.Selection is only to keep the stack of its average entropy minimum.When obtaining this stack, it becomes new input stack, and this process is restarted.Keep the interference operator that generates minimum entropy stack, and with Int ¹Be set to the interference operator of new step.When the minimum average B configuration entropy was in given critical limits, calculating stopped.At this moment, analogue measurement is measured as the squared absolute value according to its probability amplitude, the basic value that extracts from final stack.

In Figure 14, whole algorithm is restarted in the following manner:

$1.|\mathrm{input}\&rang;=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i\&rang;,$ X wherein _iBe real number at random, c _iBe random complex, satisfy

$\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\left|\right|c_i\left|\right|}^2=1;$ Generate the Int that rank are t at random ¹Unit operator;

$2.\stackrel{\&OverBar;}{A}=\left(\begin{array}{c}\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,1}\&rang;\\ \underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,2}\&rang;\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ \underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,k}\&rang;\end{array}\right),$ Generation-ε≤ε at random wherein _{I, j}≤ ε, and

$\&ForAll;i_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A200510082346.100671.png,A200510082346.100681.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,j:{\mathrm{<figure-callout\; id="1"\; label="x\; i"\; filenames="A200510082346.100601.png,A200510082346.100611.png"\; state="\{\{state\}\}">x</figure-callout>}}_{i_{}}+{\mathrm{\&epsiv;}}_{i_1,j}\&NotEqual;{\mathrm{<figure-callout\; id="2"\; label="x\; i"\; filenames="A200510082346.100671.png,A200510082346.100681.png"\; state="\{\{state\}\}">x</figure-callout>}}_{i_{}}+{\mathrm{\&epsiv;}}_{i_2,j};$

$3.\stackrel{\&OverBar;}{B}=\left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Int"\; filenames="A200510082346.100601.png,A200510082346.100611.png"\; state="\{\{state\}\}">Int</figure-callout>}}^1\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,1}\&rang;\\ {\mathrm{<figure-callout\; id="2"\; label="Int"\; filenames="A200510082346.100671.png,A200510082346.100681.png"\; state="\{\{state\}\}">Int</figure-callout>}}^2\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,2}\&rang;\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{Int}}^k\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_i|x_i+{\mathrm{\&epsiv;}}_{i,k}\&rang;\end{array}\right)=\left(\begin{array}{c}\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_{i,1}^{\&prime;}|x_i+{\mathrm{\&epsiv;}}_{i,1}\&rang;\\ \underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_{i,2}^{\&prime;}|x_i+{\mathrm{\&epsiv;}}_{i,2}\&rang;\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ \underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_{i,k}^{\&prime;}|x_i+{\mathrm{\&epsiv;}}_{i,k}\&rang;\end{array}\right),$ Int wherein ¹Be that rank are the positive square matrix of unit of t:

$4.|{\mathrm{output}}^{*}\&rang;=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{c}_{i,j^{*}}^{\&prime;}|x_i+{\mathrm{\&epsiv;}}_{i,j^{*}}\&rang;$ Wherein $j^{*}=\arg \left(\min \right\{\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\left|\right|c_{i,j}^{\&prime;}\left|\right|}^{2}E(x_i+{\mathrm{\&epsiv;}}_{i,j})\left\}\right);$

$5.\stackrel{\&OverBar;}{E^{*}}=\underset{i=1}{\overset{t}{\mathrm{\&Sigma;}}}{\left|\right|c_{i,j^{*}}^{\&prime;}\left|\right|}^{2}E(x_i+{\mathrm{\&epsiv;}}_{i,j^{*}})$

6. if ＜E ' and information risk increment are less than the quantity △ that sets up in advance, then from distributing $(x_i+{\mathrm{\&epsiv;}}_{i,j^{*}},{\left|\right|{c^{\&prime;}}_{i,j^{*}}\left|\right|}^2)$ The middle x that extracts _I*+ ε _{I*, j*}

Otherwise, will | input be set to | output ^*, int ¹Be set to int ^J*, turn back to step then

Note 2. Step 6 comprises the method for accurate estimation and reliable measurements successful result.

Estimate the simulation of expression quantum search algorithm by information flow analysis, information risk increment and entropy standard:

1) the quantum door G with relevant input vector canned data is applied to system state, minimize through

Gap between allusion quotation Shannon entropy and the quantum Feng Neumann entropy;

2) repeat described application, to calculate (estimation) information risk increment (seeing note 3);

3) measure described base vector, to estimate average entropy;

4) successfully decoded result's described base vector is to calculate the time that stops when the minimum average B configuration entropy is in given critical limits.

Note 3.Calculate (estimation) information risk increment according to following formula:

$-\sqrt{r\left(W^2\right)2I(\tilde{p}:p)}\&le;(\mathrm{\&delta;r}=\tilde{r}-r)\&le;\sqrt{\tilde{r}\left(W^2\right)2I(p:\tilde{p})}$

Wherein:

W is a loss function;

R (W ²)=∫ ∫ W ²P (x, θ) dxd θ is corresponding probability density function p (x, average risk θ);

X=(x ₁..., x _n) be the vector of measured value;

θ is a unknown parameter;

· $I(p:\tilde{p})=\&Integral;\&Integral;p(x,\mathrm{\&theta;})\ln \frac{p(x,\mathrm{\&theta;})}{\tilde{p}(x,\mathrm{\&theta;})}\mathrm{dxd\&theta;}$ For relative entropy ( Informational divergence Kullback- LeiblerMeasure).

As mentioned above, GA searches for globally optimal solution in single solution space.In order to be expressly understood the implication of these words, further be explained as follows.

Figure 15 represents the detailed structure of GA and QSA algorithm.In the GA search, solution space 301 is led to initial position (input) 302.Use binary coded patterns 310 that initial position 302 is encoded to binary string.To be applied to coded strings such as selection 303, intersection 304 and the GA operator that makes a variation 305, to generate population.By objective function 306 (as objective function), search the globally optimal solution in single space 301 based on minimum entropy throughput rate or some other required attribute.

Example." single solution space " comprises all possible coefficient gain of the PID controller of the equipment under the random disturbance, and wherein random disturbance has the fixedly statistical property as related function and probability density function.After the kinematic behavior of utilizing the equipment under the GA stochastic simulation arbitrary excitation, we only can obtain to have the fixedly optimum coefficient gain of the intelligent PID controller of the arbitrary excitation of statistical property.Since it is so, we are defined as 301 to " the single space of feasible solution ".If we use arbitrary excitation with another kind of statistical property on equipment, then intelligent PID controller can not utilize fixedly KB realization control law.Since it is so, we are new feasible solution definition space 350.

Note 4.If we need be from the general look-up table of the intelligent PID controller of many single solution spaces, then use GA can not provide final correct result (the GA operator does not comprise that stack is relevant with quantum such as braiding).GA provides the globally optimal solution on the single solution space.Since it is so, we have lost the important information of the statistic correlation between the coefficient gain in the relevant general look-up table.

On the contrary, in QSA shown in Figure 15, use N solution space of a group 350 to create an initial position (input) 351.Such as stack 352, braiding 353 and disturb the quantum operators 354 to act on this initial position, measure to generate.Use Hadamard conversion 361 (bit operatings) to create stack.Create braiding by controlled NOT (CNOT) operation 362 (2 bit operatings).Create interference by quantum Fourier transform (QFT) 363.By using quantum operators, find the general optimum solution of all solution spaces in the covering group 350.

Note 5.Therefore, classical selection course roughly is similar to the quantum process of creating stack.Classical intersection process roughly is similar to quantum braiding process.Classical mutation process roughly is similar to the quantum interference process.

Figure 16 represents the general structure of QSA, and this structure has conceptual level 400, structural level 401, hardware level 402 and software levels 403.

At conceptual level 400, provide original state 410 to processing block 420, processing block 420 creation state StackThe stack of state is offered processing block 430, the latter to BraidingUnit operator U is provided _fThe output of processing block 430 offered answer piece 440, and the latter calculates answer Disturb To answer piece 440 and offer observation/measurement piece 460.

At structural level, be a series of quantum bit (qubit) with input coding, in original state (as the logic zero state), prepare quantum bit and offer Hadamard transformation matrix 421, to generate stack.The stack of matrix 421 is offered the operator U that generates braiding _f, wherein in generalized case, operator U _fBe the separating of Schr  dinger equation in the processing block 431.The output of processing block 431 is offered quantum Fourier transform (QFT), so that interference to be provided.The output of QFT 441 is offered transformation matrix 451.Output the separating as the quantum searching process with maximum probability amplitude 461 of transformation matrix 451 is provided.

At hardware level, utilize revolving door 422 to generate stack 420, realize operator U _fAs the result of elementary gate operation and CNOT door 432, realize the result of QFFT 441 as Hadamard and arrangement (P) operator door, use revolving door 452 to realize transformation matrix 451.

Figure 17 represents the architecture of QSA, and architecture comprises the order that begins from the original state that obtains by the establishment stack.Braiding is applied to stack, and stack is used itself quantum concurrency as the correlative subsystem with woven condition.Concurrency is folding when introducing interference, with the stack by the QFFT generating solution.By likening classical double slit experiment to amount of logic child-operation and quantum searching operation, Figure 17 represents above-mentioned processing.

Note 6.In classical double slit, the particle with initial overlaying state is created in the source.This is similar to the quantum algorithm operation that Hadamard (revolving door) conversion is applied to the initial quantum bit of eigenstate.Turn back to double slit, utilize particle to generate braiding by seam.This is equivalent to applying unit operator U _fThe process that stack is handled.Turn back to double slit once more, when the braiding particle reaches the photographic film that is placed on the seam back, when generating jamming pattern (stack of separating), generate and disturb.This is equivalent to QFFT.At last, select required separating to be equivalent to from QFFT, to select maximum probability (that is, form on the film bright line section).

Figure 18 represents to use QSA with GA or FNN.Original state generator 604 is worked with GA605 and fuzzy neural network (FNN) 603 (optional), to generate one group of original state.Original state is offered Hadamard conversion 602, to generate the stack 601 of state.The stack of classical state is offered processing block 606, and the latter introduces braiding by using the operator such as CNOT.The output of processing block 606 is offered the interference of disturbing piece 607, the latter to use QFFT calculating woven condition.To disturb the output of piece 607 to offer measurement/observation piece 608, the latter selects required separating from the stack of separating that piece 607 calculates.

The output of measurement/observation piece 608 is offered decision block 609.The input of decision block 609 decision original state generators 604, and the fresh target function (optional) of GA 605.Decision block 609 also can provide data to decode block 610, or receives data from piece 610.Decode block 610 can communicate with sensor, other control system, user etc.

Law according to quantum theory obtains basic quantum calculation, and wherein information can be carried out on the realization equipment at actual physics and calculate for to encode in the state of physical system.

The following instantiation of single solution space of arbitrary excitation " reverse " fuzzy controller of explanation controlling object.

Example.Utilize GA and use the stochastic simulation of random Gaussian signal, receive the KB of intelligent suspension control system as highway.After utilizing fuzzy controller to carry out on-line simulation, we use other two kinds of actual highway signals (Japanese highway survey).The analog result at expression pitch angle in Figure 20 and 21.Figure 20 represents that the change of the statistical property of highway (seeing Figure 19) reverses the single solution space of fuzzy controller.

Since it is so, we must utilize GA to repeat simulation, and use other single solution space with objective function, and objective function is as the entropy production of the fuzzy controller of the non-Gaussian excitation with controlling object.

In more detail, we use the kinematic behavior of GA with minimizes dynamic system (equipment), and minimize entropy throughput rate.We use different types of random signal (as random disturbance), and random signal is represented the highway distribution situation.Some signal is to measure on the actual highway of Japan, and some signal generates by using stochastic simulation, and wherein stochastic simulation has the shaping filtrator based on FPK (Fokker-Planck-Kolmogorov) equation.In Figure 19, three kinds of typical highway signals have been represented.The change rate of Figure 190 1,1902,1903 expression signals.With the mode of the simulation 50kph speed of a motor vehicle, the hour range of dispensed.Preceding two signals (HouseWC) and (HouseEC) be the actual highway of measuring in Japan.The 3rd signal has fixedly Gauss's highway of the stochastic simulation acquisition of the related function of kind for utilizing.We see that the kinematic behavior of above-mentioned highway similar (seeing figure (A)) is but the statistical property of the statistical property of HouseWC highway and Gauss's highway and HouseEC highway differs widely (seeing figure (B)).The HouseWC highway is represented so-called non-Gauss (colour) statistic processes.

The greatest differences of the statistical property of highway signal causes the diverse response of dynamic system, therefore, needs different controlling schemes.

Figure 20 and 21 expression suspension (equipment) are to the power and the heat power response of above-mentioned excitation.The kinematic behavior at the pitch angle of vehicle on figure (a) expression HouseWC (curve 1), HouseEC (curve 2) and Gauss's (curve 3) highway.By using the knowledge base of Gauss's highway signal acquisition, then knowledge base is applied to HouseWC and HouseEC highway as the look-up table of fuzzy controller.We see, the system responses with highway of identical characteristics is similarly, this means that GA finds the optimum solution of the signal shape with Gauss feature, but are diverse signals to the response of system with HouseWC highway.For non-Gauss's highway, the brand-new control GA strategy that we need be different with above-mentioned response, that is, it needs separating of different single solution spaces.In phase diagram (figure (b)), the easier difference of seeing system responses.

Yet, be preferably in many solution spaces and search for globally optimal solution, to search " general " optimum solution.The quantum genetic algorithm search provides the ability of searching for many spaces simultaneously (the following describes).

Fig. 2 represents the improved form of intelligence control system of the present invention, wherein inserts quantum genetic searching algorithm (QGSA) between GA and FNN.QGSA searches for several solution spaces simultaneously, so that search general optimum solution, that is, is separating of the optimum solution of all solution spaces.

The accelerator of quantum algorithm

Below explanation is used for the hardware accelerator of simulation quantum algorithm on classic computer.

Accelerator has modular structure, thereby can be generalized to complex model.From known module, make up its target for being dropped to the architecture of minimum level the required exponential time of simulation of the quantum algorithm on the classic computer.The major advantage of this method be can be in the genetic algorithm field logic of use amount subalgorithm, started new quantum genetic searching algorithm branch.

Hardware accelerator is by constituting with lower member:

Scrambler, code translator: these two is the actual interface with the classical equipment that is connected to accelerator.

Quantum piece: comprise the non-classical operation that all will be carried out.It is made up of quantum door and measurement door.

The quantum door: be the core of accelerator, it is made up of three modules, and three modules are with quantum mode mixed information.Three modules are:

Laminating module: depend on the problem types that will solve.

Braiding module: read information from scrambler.

Interference module: its operation of iteration is separated until obtaining.

Measure door: extract quantum information by a series of pseudorandom routine.

Final information is sent to code translator.

The stack, braiding and the interference piece that are fit to the dimension of quantum bit number, the quantum door of composition general type.Then " preparation " above three so that realize required algorithm.Figure 23 and 27 describes the example of the quantum door of realizing the Grover algorithm, and Figure 24 describes the example of the quantum door of realizing the Deutsch-Jozsa algorithm.

Below explain in detail the method for designing of all pieces that comprise in this pattern.

Stack: in this step, need the tensor product between the vector.Rely on the single construction equipment of electronic multiplier and multiplex (MUX) to realize this operation.Can use ROM cell to make up the H matrix.

Braiding: the large matrix U that can use the EPROM equipment making to make amendment according to F _F

Disturb: the identical piece of kind of the piece that need need with stack.Just connect different.

Two examples of following recommended amounts cervical orifice of uterus usage (seeing Figure 24-29).Figure 24 to 26 is the decision-making with respect to the Deutsch-Jozsa quantum algorithm, and Figure 27 to 29 is the structured data library searching with respect to the Grover quantum algorithm.

As from above pattern, seeing, the core of each subsystem is to realize the tensor product door of the tensor product between a pair of input vector, thereby export a matrix, the component of matrix is the product of the component of an input vector and another vector components is formed all different right values.By the many multipliers of suitable connection, can realize the tensor product door with example, in hardware.

The quantum door of this paper performance only has two quantum bits, still, can improve them easily.In fact, each the tensor product door that adds in the subsystem provides doubling of quantum bit in this, if jointly suitably adjust the single worker's piece of the multiplex (MUX) who exists in the scalar product.

Note that as if the interference piece in the proposed algorithm different with the architecture viewpoint.In fact, when making up the door of only realizing this type of algorithm, the simplicity of Deutsch-Jozsa algorithm allows us to adopt simple structure.Yet the structure that Grover disturbs is more common, and also can realize the Deutsch-Jozsa algorithm.This fact provides the general feature of logic gate second example.

For quantum genetic searching algorithm structure,, can obtain its hardware components from Grover braiding and interference piece easily by simple modification.In fact, its unique difference is to generate at random all matrixes, but all keeping them in all situations is unit matrix.

Figure 30 and 31 describes the example of the possible embodiment that weaves operator and random disturbance subsystem at random.The core of braiding subsystem is the dot product door, and the dot product door is realized the dot product between the identical a pair of input vector of its number of components, thus output as the product of the paired value of each component of input vector and value.By using at least one multiplier and a totalizer, can realize the dot product door with hardware mode, wherein multiplier is calculated to be the product to value, this product and totalizer adds up.

The algorithm that is used for search database

The use of quantum genetic searching algorithm of the present invention is satisfactory, has both made the closest value Y that gathers X as belonging in the search database ₀Project x _iAlgorithm.

As mentioned above, can search problem be restated into Grover problem all the time.Suppose quantum genetic searching algorithm of the present invention then, can to use quantum genetic search algorithm to solve search problem by according to the smart stacking of Grover algorithm, braiding and interference operator as the especially effective quantum algorithm of a class.

Or rather, utilize following method to define in the search database and belong to the closest value Y that gathers X ₀Project x _iAlgorithm:

Represent to belong to projects of gathering X with vector form, generate the initial sets of vector;

Calculate second group of vector, its method is according to the vector in the initial sets of Grover quantum search algorithm linear superposition vector;

According to the Grover quantum search algorithm, second group of vector carried out parallel knit operation at random and the random disturbance operation of determining number of times, generate many vectors of the project of expression set X;

Each end value and the objective function of parallel computation are connected, and wherein objective function is necessary for above end value and expectation value Y ₀Between difference;

According to genetic algorithm, use objective function that the end value of parallel computation is carried out selection operation;

Sign is as the search item x of final selection result _i

The method that is used for control procedure and relevant controlling device

Can be used for control by control signal (U ^*) use QGSA in the method for the process (equipment) that drives.As the function of parameter adjustment signal (CGS) and error signal (ε), calculation control signal (U ^*), wherein obtain error signal as difference between process status (X) and the reference signal state (Y).

The purpose of this method is certain physical quantity is dropped to minimum value, and this physical values for example is the entropy output of controlled process.In order to realize this target, by handling described process status (X) and described control signal (U ^*) paired value, induced representation is wanted the signal (s) of minimized physical quantity.

The favourable use quantum of method of the present invention genetic search algorithm is to search Optimal Control signal (U ^*), thereby input process is controlled.Generate this type of control signal by controller, controller has adjustable transmission characteristic, and the latter is as the function of the value vector of the parameter of distributing to controller.

Can restate the problem of control procedure with the following methods: search the value vector that certain quantity is dropped to minimum level, promptly search certain vector function is dropped to minimum vector, wherein quantity is the function of described vector.

Therefore, genetic algorithm is very important to the method for control procedure obviously, and how to use quantum genetic search algorithm effectively in this type of is used.

At first, from described control signal (U ^*) one group of different value in regular correction signal (k2), this signal minimizes needs minimized described derivation signal (s).

By the quantum genetic searching algorithm being applied to represent many different control signal (U ^*) one group of vector, correction signal (k2) use to want minimized quantity as objective function.

At last, with above correction signal (k2) feed-in fuzzy neural network, the latter generates described parameter adjustment signal (CGS), and this signal is offered fuzzy processor with error signal (ε), and fuzzy controller is adjusted the transmission characteristic of controller.

Want minimized physical quantity by changing, can realize the many different embodiments of the method, for example, minimize difference or Heisenberg uncertainty between Shannon entropy and Feng's Neumann entropy, or rather, for internal combustion engine, minimize the entropy output of heat power process.

By disturbing and the braiding operator according to quantum problem selection arbitrarily, also can adopt quantum genetic searching algorithm of the present invention suitably, for example, can select above operator according to Grover problem or Shor problem.

Preferred forms of the present invention is, with representing many different control signal (U ^*) one group of vector operation genetic algorithm, generating provisional correction signal (K), this signal is generated meticulously by the quantum genetic searching algorithm.This embodiment is best, and reason is the converges faster of quantum genetic searching algorithm.

Fig. 2 describes the structure of the best hardware embodiment of method of the present invention.With control signal U ^*The process (equipment) that drives places classical feedback control loop and PID controller.PID generates the drive signal U that depends on error signal ^*, as the state Y function calculation error signal of status of processes X and reference signal.

Circuit block drive signal s, the signal s minimized quantity of indicating, this quantity can be entropy output, for example, by the state X and the control signal U of processing procedure ^*The value calculated of paired value.

Signal s can be input to circuit QGSA, the latter realizes the quantum genetic searching algorithm, output calibration signal k2, and perhaps at first by circuit GA supervisory signal s, circuit GA realizes genetic algorithm, the latter generates a provisional correction signal K, with input QGSA circuit.

In structure shown in Figure 2, although realize that the circuit of GA is optional, its reason is and can usually, realizes that the circuit GA of genetic algorithm appears in the system architecture with quantum genetic searching algorithm of the present invention " popularization " to genetic algorithm.

This is because the GA circuit generates the structured data of quantum genetic search algorithm, thereby this convergence of algorithm is faster.Usually, can be stated as, genetic algorithm generates the optimum solution of single solution space: this means that we can compress the information in the single solution space, and guarantee the security of the information parameter among the signal K by realizing genetic algorithm GA circuit.Quantum searching on the structured data guarantees that searching success separates, and has more high probability and accuracy than the search on the non-structured data.

Fuzzy neural network FNN generates a drive signal, and this signal depends on the value of QGSA output calibration signal k2, and fuzzy controller FC adjusts the transmission characteristic of classical PID controller, and the PID controller depends on the value of drive signal and error signal.

The training system of the intelligence control system that its number of sensors reduces

The quantum genetic searching algorithm can be used to realize intelligence control system, compares with the optimum intelligence control system of prior art, and this control system can utilize less sensor to come the driving process.

Using fuzzy neural network (FNN) before, " training " stage is essential, and FNN learns to drive the method for controlled process in this stage.By using many different sensors of physical quantity, carry out " training " at equipment or repair center, wherein physical quantity is the operation characteristic of process.Usually, in this stage, use unsupported several sensors in the normal running of this process.Given this, must teach FNN utilizes less sensor (that is, only utilizing the sensor that exists in the normal running of this process) to drive the method for this process.

Can utilize Figure 32 and 33 architectures of describing in detail to realize this target.Functional block and the signal of table 4 for occurring among the above-mentioned figure.

The general structure of control system is simplified in Figure 32 and 33 expressions.Figure 32 is a block diagram, and control system 480 and optimal control system 420 are simplified in expression.Use optimal control system 420 and optimizer 440 and 460 training of sensor information compensator to simplify control system 480.In Figure 32, desired signal (representing required output) is offered the input of optimal control system 420, and the input of simplifying control system 480.Optimal control system 420 has m sensor, and they provide output sensor signal x _bWith optimum control signal x _aSimplify control system 480 output sensor signal y is provided _bWith simplify control signal y _aSignal x _bAnd y _bThe data that comprise k sensor, wherein k≤m-n.Usually, this k sensor is a uncurrent sensor between sensing system 422 and 482.With signal x _bAnd y _bOffer first input and second input of subtracter 491.Subtracter 491 is output as signal epsilon _b, ε wherein _b=x _b-y _bWith signal epsilon _bOffer the sensor input of sensor compensation device 460.With signal x _aAnd y _aOffer first input and second input of subtracter 490.Subtracter 490 is output as signal epsilon _a, ε wherein _a=x _a-y _aWith signal epsilon _aOffer the control signal input of sensor compensation device 460.The control information output of sensor compensation device 460 is offered the control information input of optimizer 440.The sensor information output of sensor compensation device 460 is offered the sensor information input of optimizer 440.Simultaneously, the sensor signal 483 of simplifying control system 480 is offered the input of optimizer 440.The output of optimizer 440 provides instructional signal 443 to the input of simplifying control system 480.

In the following description, offline mode is often referred to calibration mode, wherein utilizes the optimal set operation controlling object 428 (with controlling object 488) of m sensor.In one embodiment, in equipment or repair center, move offline mode, wherein use additional sensor (that is, belong to the m group but do not belong to the sensor of n group) training FNN1 426 and FNN2 486 at equipment or repair center.Online mode is often referred to operational mode (that is, normal mode), only utilizes n group operating sensor system in this pattern.

Figure 33 is a block diagram, represents the functional block among Figure 32 in detail.In Figure 33, utilize the output of the sensor groups m 422 with m sensor that output signal x is provided _b, m=k+n wherein.The information of sensing system m 422 is for having optimal information content I ₁A signal (sets of signals).In other words, information I ₁Information for the complete or collected works of m sensor in the sensing system 422.The output of control assembly 425 provides output signal x _aWith output signal x _aOffer the input of controlling object 428.The output of controlling object 428 is offered the input of sensing system 422.To organize the information I of sensor from k _kOffer the online learning input of fuzzy neural network (FNN1) 426, and the input of first genetic algorithm (GA1) 427.N in the autobiography sensor system 422 organizes the information I of sensor in the future _n, offer the input of controlling object model 424.The off line of algorithm GA1 427 outputs is adjusted signal, and the off line that offers FNN1 426 is adjusted the signal input.FNN 426 output be controlled to be control signal x _a, this signal is offered the control input of controlling object 428.Controlling object model 424 and FNN 426 constitute optimum fuzzy control unit 425 together.

Simultaneously, in Figure 33, sensor compensation device 460 comprises multiplier 462, multiplier 466, information calculator 464 and information calculator 468.In online (normally) pattern, use multiplier 462 and information calculator 464.Provide multiplier 466 and information calculator 468 to be used for the off line inspection.

Signal epsilon with totalizer 490 outputs _a, offer first input and second input of multiplier 462.With the output of multiplier 462 (is signal epsilon _a ²) offer the input of information calculator 464.Information calculator 464 is calculated H _a(y)≤I (x _a, y _a).Information calculator 464 is output as the information standard of a relevant accuracy and reliability, I (x _a, y _aThe maximal value of) → simplify control signal in the control system.

Signal epsilon with totalizer 491 outputs _b, offer first input and second input of multiplier 466.With the output of multiplier 466 (is signal epsilon _b ²) offer the input of information calculator 468.Information calculator 468 is calculated H _b(y)≤I (x _b, y _b).Information calculator 468 is output as the information standard of a relevant accuracy and reliability, I (x _b, y _bThe maximal value of the output signal of the controlling object that) → number of sensors reduces.

Optimizer 440 comprises 444 and entropy models 442 of one second genetic algorithm (GA2).With signal I (x _a, y _aThe maximal value of) → information calculator 464 offers first input of the algorithm (GA2) 444 in the optimizer 440.From the output of thermodynamic model 442, provide entropy signal S → minimum value to second input of genetic algorithm GA2 444.With signal I (x _b, y _bThe maximal value of) → information calculator 468 offers the 3rd input of algorithm in the optimizer 440 (GA2) 444.

Offer the signal I (x of the first and the 3rd input of algorithm (GA2) 444 _a, y _a) → maximal value and I (x _b, y _b) → maximal value is an information standard, offers the entropy signal S (k of second input of algorithm (GA2) 444 ₂) minimum value is the physical criterion based on entropy.Algorithm GA2 444 is output as the instructional signal of the FNN2 486 that the following describes.

Simplifying control system 480 comprises and simplifies sensor groups 482, controlling object model 484, FNN2486 and controlling object 488.When moving in specific off line inspection (checking) pattern, sensing system 482 also comprises k group sensor.Controlling object model 484 and FNN2 486 constitute together and simplify fuzzy control unit 485.The output of controlling object 488 is offered an input of sensor groups 482.The I of sensor groups 482 ₂Output comprises the information from sensor groups n, wherein n=(k ₁+ k ₂)＜m satisfies I ₂＜I ₁With information I ₂, offer the adjustment input of FNN2 486, the input of controlling object model 484, and the input of entropy model 442.The instructional signal 443 of algorithm GA2 444 is offered the instructional signal input of FNN2 486.FNN2 486 output be controlled to be signal y _a, this signal is offered the control input of controlling object 488.

Controlling object model 424 and 484 can be complete model or partial model.The complete mathematical model representation of controlling object is one and comprises the differential equation that dissipates and handle, and partial model is a model that does not comprise the complete analysis description.

For example, for hanging control system, nonlinear equation that can write through system " vehicle+suspension " uses the dissipative term of nonlinear equation to calculate entropy throughput rate with analysis mode then, and for Engine Control System, it is disabled that the parsing of mathematical model is described.

Although Figure 32 and 33 represents optimal system 420 and simplifies system 480 that in the autonomous system mode system 420 and system 480 are same system usually.By deletion additional sensor and neural network training from system 420, " establishment " system 480.Therefore, controlling object model 424 is identical with 484 usually.Controlling object 428 is also identical usually with 488.

Figure 33 represents to adjust arrow mark 429 from GA1 427 to FNN1 426 and from the off line of GA2 444 to FNN2 486.Figure 33 also represents from the online learning arrow mark of sensing system 422 to FNN1 426.Adjust GA2 444 and mean the one group of coefficient of connection that changes among the FNN2 486.Change coefficient of connection (for example, using iteration backpropagation or trial and error to handle), thereby (S tends to minimum value to I for x, y) trend maximal value.In other words, from the information of GA2 444 to the code set of FNN2 486 these coefficients of transmission, (x y), and calculates S as I.Usually, in equipment or service centre, with the coefficient of connection among the offline mode adjustment FNN2 486.

Instructional signal 429 is a signal, and during utilizing the optimum control collection to handle optimal control system 420, this signal works to FNN1 426.Usually, when simplifying control system when moving, by not providing instructional signal 429 with simplifying the sensor that control system 480 uses with online mode.GA1427 adjusts FNN1 426 during offline mode.Dot and x _bAnd y _bRelevant signal wire is to represent only to use x during specific off line inspection (that is checking) pattern usually _bAnd y _bSignal.During Validation Mode, utilize the optimal set operation of sensor to simplify control system.Additional sensor information is offered optimizer 440, and optimizer 440 checkings are simplified control system 480 with required (almost best) accuracy operation.

The nonlinear dissipative mathematical model is described and number of sensors reduces stablizing and unstable controlling object of (or different sets of sensor) for having, according to information standard I (x _a, y _a) → maximal value and I (x _b, y _b) → maximal value connects the output accuracy of Control System Design and controlling object and the Calculation of Reliability of control system.According to physical criterion S (k ₂) → minimum value connects the stability and the robustness inspection of Control System Design and control system and controlling object.

In first step, use the genetic algorithm GA2 444 that has objective function, form the instructional signal 443 of fuzzy neural network FNN2 486 in the off-line simulation, wherein objective function is optimum control signal x _aWith simplify control signal y _aBetween the maximal value of interactive information.By using learning process to realize fuzzy neural network FNN2 486, learning process has error back propagation, with the adaptive learning signal, and is formed for changing the look-up table of the parameter of the PID controller in the controller 485.Thereby the required control reliability that has enough accuracy for acquisition provides adequate condition.

In second step, use has the genetic algorithm GA2 444 of objective function, realize the node correction look-up table among the FNN2486, wherein objective function is minimum entropy S or throughput rate dS/dt (calculating according to the mathematical model of controlling object 488 or the experimental result of sensor measurement information).This method provides enough accurate reliably control to stability of simplifying control system 480 and robustness.Thereby the robust intelligence control system that reduces for the design number of sensors provides adequate condition.

Needn't carry out above first and second steps by listed order (i.e. order).When the unstable object of simulation, preferably by using objective function and information standard, in above two steps of executed in parallel, wherein objective function is the physical quantity sum.

Behind the look-up table of simulation FNN2 486, on sensing system 482, change the mathematical model of controlling object 484, simplify control system and the qualitative features between the control system of simplifying with whole (optimal number) sensors with what check that its number of sensors reduces.Use has the parallel optimization among the GA2 444 of two objective functions, realizes that the overall situation of the look-up table among the FNN2 486 is proofreaied and correct.

Entropy model 442 extracts sensing system information I ₂In data, to help to determine required measured sensor number and the control controlling object 488 of being used for.

The sensor that Figure 32 and 33 expressions reduce does not comprise the generalized case the when calculating of control signal of survey sensor in the output of controlling object and information standard is more feasible.Sensor compensation device 460 computing information standards, information standard are two control signal x _aAnd y _aBetween the maximal value (as first objective function of GA2 444) of interactive information.Entropy model 442 provides physical criterion by using the information from sensor 482, and physical criterion is minimum production entropy (as second objective function of GA2 444).GA2 444 is output as the instructional signal 443 of FNN2 486, and this signal of online use is simplified control signal y with generation _aThereby, simplify control signal y _bCharacter be similar to optimum control signal x _aCharacter.Therefore, optimizer 440 provides the stability and the robustness (use physical criterion) of control, and the reliability (use information standard) with enough accuracy.

By the off line inspection, optimizer 440 provides control signal y by using new information standard from FNN2 486 _aCorrection.Because information measurement adds, so can order or executed in parallel online/offline step.In off line was checked, sensing system 482 was only being checked control signal y usually _aCharacteristic and timing, just use all the sensors.Even controlling object 488 instabilities, this method also can provide required stability and control characteristic.

For simplifying sensing system 482 (n sensor arranged), FNN2 486 preferably uses the study and the procedure of adaptation to replace fuzzy controller (FC) algorithm.

If controlling object will be worked, then use global optimizer 450 in having the varying environment of different qualities.Global optimizer 450 comprises GA2 444 and QGSA 448.The output 449 of GA2 is the input of QGSA 448.QGSA 448 is output as the instructional signal of FNN2 486.Be necessary for each single solution space and generate output 449.

Be applied to the control system of simplifying of internal combustion engine

In one embodiment, will simplify control system and be applied to internal combustion piston engines, jet engine, gas turbine engine, rocket engine etc., so that under the situation of not using the additional sensor such as oxygen sensor, provide control.

Figure 34 represents the internal combustion piston engines, and this engine has four sensors, 604, one crank angle sensors 608 of 602, one cooling-water temperature sensors of an intake air temperature sensor.The temperature that air-temperature sensor 602 is measured in the draft tube 620.The air of fuel injector 629 in draft tube 620 provides fuel oil.Draft tube 620 provides air and fuel oil to firing chamber 622.The burning driven plunger 628 of firing chamber 622 intermediate fuel oils and air mixed body.Piston 628 is connected to crank 626, thus the motion rotating crank 626 of piston 628.Crank angle sensor 606 is measured the turned position of crank 626.Cooling-water temperature sensor is measured around the water temperature of the water pipe sleeve 630 of firing chamber 622 and piston 628.The waste gas of the chamber of spontaneous combustion in the future 622 offers gas outlet 624, air and fuel oil ratio that air oil ratio sensor 608 is measured in the waste gas.

Figure 35 is a block diagram, and control system 780 and optimal control system 720 are simplified in expression.Optimal control system 720 is used for training and simplifies control system 780 together with optimizer 740 and sensor compensation device 760.In Figure 35, to the input of optimal control system 720 with simplify the input of control system 780, provide desired signal (representing required engine output).Optimal control system 720 with 5 sensors provides optimum control signal x _aWith sensor output signal x _bSimplifying control system 780 provides and simplifies control output signal y _aWith output sensor signal y _bSignal x _bAnd y _bComprise data from A/F sensor 608.With signal x _bAnd y _bOffer first input and second input of subtracter 791.Subtracter 791 is output as signal epsilon _b, ε wherein _b=x _b-y _bWith signal epsilon _bOffer the sensor input of sensor compensation device 760.With signal x _aAnd y _aOffer first input and second input of subtracter 790.Subtracter 790 is output as signal epsilon _a, ε wherein _a=x _a-y _aWith signal epsilon _aOffer the control signal input of sensor compensation device 760.The control information output of sensor compensation device 760 is offered the control information input of optimizer 740.The sensor information output of sensor compensation device 760 is offered the sensor information input of optimizer 740.Simultaneously, the sensor signal 783 of simplifying control system 780 is offered the input of optimizer 740.The output of optimizer 740 provides instructional signal 747 to the input of simplifying control system 780.

Output by sensing system 722 provides output signal x _b, system 722 has 5 sensors, comprises intake air temperature sensor 602, cooling-water temperature sensor 604, crank angle sensor 607 and air oil ratio sensor 608.From the information of sensing system 722 for having optimal information content I ₁One group of signal.In other words, information I ₁Be information from all 5 sensors in the sensing system 722.

Output by control assembly 725 provides output signal x _aWith output signal x _aOffer the input of engine 728.The output of engine 728 is offered the input of sensing system 722.Will be from the information I of A/F sensor 608 _K1Offer the online learning input of fuzzy neural network (FNN) 726, and the input of first genetic algorithm (GA1) 727.Will be from the information I of four groups of sensors except that A/F sensor 608 _K1, offer the input of engine model 724.The off line of algorithm GA1 727 outputs is adjusted signal, and the off line that offers FNN 726 is adjusted the signal input.FNN 726 output be controlled to be fuel Injection Control signal U ₁, this signal is offered the control input of engine 728.Signal U ₁Also be signal x _aEngine model 724 and FNN 726 constitute optimum control parts 725 together.

Sensor compensation device 760 comprises multiplier 762, multiplier 766 and information calculator 764.In online (normally) pattern, use multiplier 762 and information calculator 764.Provide multiplier 766 and information calculator 768 to be used for the off line inspection.

Signal epsilon with totalizer 790 outputs _a, offer first input and second input of multiplier 762.With the output of multiplier 762 (is signal epsilon _a ²) offer the input of information calculator 764.Information calculator 764 is calculated H _a(y)≤I (x _a, y _a).Information calculator 764 is output as the information standard of a relevant accuracy and reliability, I (x _a, y _a) → maximal value.

Signal epsilon with totalizer 791 outputs _b, offer first input and second input of multiplier 766.With the output of multiplier 764 (is signal epsilon _b ²) offer the input of information calculator 768.Information calculator 768 is calculated H _b(y)≤I (x _b, y _b).Information calculator 768 is output as the information standard of a relevant accuracy and reliability, I (x _b, y _b) → maximal value.

Optimizer 740 comprises 744 and heat powers of one second genetic algorithm (GA2) (entropy) model 742.With signal I (x _a, y _aThe maximal value of) → information calculator 764 offers first input of the algorithm (GA2) 744 in the optimizer 740.From the output of thermodynamic model 742, provide entropy signal S → minimum value to second input of algorithm (GA2) 744.With signal I (x _b, y _bThe maximal value of) → information calculator 768 offers the 3rd input of algorithm in the optimizer 740 (GA2) 744.

Offer the signal I (x of the first and the 3rd input of algorithm (GA2) 744 _a, y _a) → maximal value and I (x _b, y _b) → maximal value is an information standard, offers the entropy signal S (k of second input of algorithm GA2 744 ₂) → minimum value is the physical criterion based on entropy.Algorithm GA2 744 is output as the instructional signal of FNN 786.

Simplifying control system 780 comprises and simplifies sensing system 782, engine model 784, FNN 786 and engine 788.Simplify sensing system 782 and comprise all engine sensor in the sensing system 722 except that A/F sensor 608.When moving in specific off line checking mode, sensing system 782 also comprises A/F sensor 608.Engine model 784 and FNN 786 constitute together and simplify control assembly 785.The output of engine 788 is offered an input of sensor groups 782.The I of sensor groups 782 ₂Output comprises from 4 sensor informations, satisfies I ₂＜I ₁With information I ₂Offer the input of controlling object model 784, and the input of thermodynamic model 742.With the instructional signal 747 of algorithm GA2744, offer the instructional signal input of FNN 786.Control signal U is sprayed in being controlled to be of FNN 786 outputs ₂, this signal also is signal y _a

The operation of system shown in Figure 35 is similar to the operation of the system shown in Figure 32 and 33 in many aspects.

Use entropy production with from cooling-water temperature sensor 604 (T ^W) and air-temperature sensor 602 (T ^A) temperature information between heat power relation, structure thermodynamic model 742.Use following relational expression to calculate entropy and produce S (T ^W, T ^A):

$S=c\frac{{\left[\ln \left(\frac{T^W}{T^A}\right)\right]}^2}{\mathrm{\&Delta;\&tau;}-\ln \left(\frac{T^W}{T^A}\right)}---\left(16\right)$

Wherein Δ τ is the cycle of finite process.

Outside between two kinds of free positions is than the satisfied following formula of merit:

$I(T^i,T^f,{\mathrm{\&tau;}}^i,{\mathrm{\&tau;}}^f)=c(T^i-T^f)-{\mathrm{cT}}^e\ln \frac{T^i}{T^f}-c{T}^e\frac{{\left[\ln \frac{T^i}{T^f}\right]}^2}{{\mathrm{\&tau;}}^f-{\mathrm{\&tau;}}^i-\ln \frac{T^i}{T^f}}----\left(17\right)$

In equation (17), because T ⁱ=T ^WAnd T ^f=T ^ASo the smallest positive integral of entropy production is:

$S_{\mathrm{\&sigma;}}=c\frac{{\left[\ln \frac{T^W}{T^A}\right]}^2}{\mathrm{\&Delta;\&tau;}-\ln \left(\frac{T^W}{T^A}\right)},$ Δ τ=τ wherein ^f-τ ⁱ(18)

Function in the equation (17) satisfies reverse Hamilton-Jacobi equation.

When representing the part engine model, in Figure 36, use QGSA in the mode of A/F ratio at random (constraint control).This means, utilize different density probability function (Gauss, non-Gauss evenly distribute, Rayleigh distribution etc.) to simulate the statistical property of A/F ratio at random.

Claims (14)

1. the training system of the intelligence control system of its number of sensors minimizing comprises

Have the intelligence control system of the sensor that ascertains the number (m), comprise

The duplicate of control procedure (428),

Fuzzy control unit (425), these parts generate the drive signal (x that is input to described reproduction process (428) _a),

The sensor of first group of second number (k), its number is identical with the status number of described reproduction process, and this group sensor generates the sensor signal (x that is fed to described fuzzy control unit _b),

The sensor of second group of the 3rd number (k1), its number is identical with the status number of described reproduction process, and this group sensor generates second sensor signal (4222) that is fed to described fuzzy control unit,

The sensor (k2) of the 3rd group of the 4th number, its number is identical with the status number of described reproduction process, and this group sensor generates the 3rd sensor signal (4221),

Realize the circuit block of first genetic algorithm (GA1), calculate the instructional signal that is input to described fuzzy control unit (425) according to described the 3rd sensor signal (4221);

The intelligence control system of utilizing the sensor (n) of the 5th number to train comprises

Control procedure (488),

Second fuzzy control unit (485), these parts generate the second drive signal (y that is input to described reproduction process (488) _a),

The duplicate of the sensor of described first group of described second number (k), its number is identical with described status of processes number, and this group sensor generates four-sensor signal (y _b),

The duplicate of the sensor of described second group of described the 3rd number (k1), its number is identical with described status of processes number, and this group sensor generates the 5th sensor signal (4822) that is fed to described second fuzzy control unit (485),

The duplicate of the sensor (k2) of described the 3rd group of described the 4th number, its number is identical with the status number of described process (488), and this group sensor generates the 6th sensor signal (4821),

Generate the circuit block of signal (S[k]) according to described the 5th sensor signal (4821), signal (S[k]) the minimized physical quantity of indicating (s),

Global optimizer (450) is according to described signal (S[k]) with represent the described first drive signal (x respectively _a) and the described second drive signal (y _a) between interactive information and described sensor signal (x _b) and described four-sensor signal (y _b) between a pair of signal of interactive information, derive the instructional signal (443) of described second fuzzy controller (485);

Sensor information compensator (450), this compensator calculate represents the described first drive signal (x respectively _a) and the described second drive signal (y _a) between interactive information and described sensor signal (x _b) and described four-sensor signal (y _b) between a pair of signal of interactive information.

2. the training system of claim 1, wherein said global optimizer (450) is a functional block, it utilizes second genetic algorithm to derive described instructional signal (443).

3. the training system of claim 1, wherein said global optimizer (450) is a functional block, it utilizes the described quantum genetic searching algorithm of claim 1 to derive described instructional signal (443).

4. claim 2 and 3 training system, wherein said global optimizer (450) is a functional block, as the net result of using described quantum genetic searching algorithm in the output of described second genetic algorithm, derives described instructional signal (443).

5. according to the training system of one of claim 1 to 4, wherein said will minimized physical quantity be the entropy production of described process (488).

6. the training system of any claim of claim 1 to 5, wherein

Described control procedure (488) is an internal combustion engine, and described reproduction process (428) is the duplicate of described internal combustion engine,

Described first group of sensor comprises an air oil ratio sensor,

Described second group of sensor comprises a crank angle sensor and a pressure transducer,

Described the 3rd group of sensor comprises an air-temperature sensor and a cooling-water temperature sensor.

7. the training system of any claim of claim 1 to 5, wherein

Described control procedure (488) is a vehicle suspension system, and described reproduction process (428) is the duplicate of described vehicle suspension system,

At least one group of described sensor comprises that at least one belongs to the sensor of the sensor groups of being made up of position transducer, slant angle sensor and roll angle sensor.

8. the method for the fuzzy control unit (485) of a training smart control system (480) comprises

Control procedure (488),

Fuzzy control unit (485), these parts generate the first drive signal (y that is input to described reproduction process (488) _a),

The sensor of first group of first number (k), its number is identical with the status number of described process (488), and this group sensor generates first sensor signal (y _b),

The sensor of second group of described second number (k1), its number is identical with the status number of described process (488), and this group sensor generates second sensor signal (4822) that is fed to described fuzzy control unit (485),

The sensor (k2) of the 3rd group of the 3rd number, its number is identical with the status number of described process (488), and this group sensor generates the 3rd sensor signal (4821),

Generate the circuit block of signal (S[k]) according to described the 3rd sensor signal (4821), signal (S[k]) the minimized signal (s) of indicating,

Global optimizer (450) generates the interim instructional signal (442) of described fuzzy control unit (485),

Use the control system (420) of the duplicate (428) of described control procedure to comprise

The duplicate of described control procedure (428),

Control assembly (425), these parts generate the second drive signal (x that is input to described reproduction process (428) _a),

The duplicate of described first, second, third group of described first (k), second (k1), the 3rd (k2) number sensor, its number status number with described reproduction process (428) respectively is identical, and these sensors generate the 4th (x that is fed to described control assembly respectively _b), the the 5th (4222) and the 6th (4221) sensor signal,

It is characterized in that may further comprise the steps:

Utilize the signal of the outside required output that provides of expression, as the input of two control system (480,420);

Calculate the described first drive signal (y _a) and the second drive signal (x _a) the interactive information (I1) of paired value;

Calculate described first sensor signal (y _b) and four-sensor signal (x _b) the interactive information (I2) of paired value;

Utilize the input of final instructional signal (443) as described fuzzy control unit (485), function as the interactive information (I2) of the interactive signal (I1) of described interim instructional signal (442), described drive signal and described sensor signal calculates final instructional signal (443).

9. the method for claim 8 wherein by using objective function that described interim instructional signal (442) is carried out genetic algorithm, derives described final instructional signal (443), objective function depend on described interactive information value (I1, I2).

10. the method for claim 8, wherein by using objective function that described interim instructional signal (442) is carried out the described quantum genetic searching algorithm of claim 1, derive described final instructional signal (443), objective function depend on described interactive information value (I1, I2).

11. the method for claim 9, wherein by using objective function that described interim instructional signal (442) is carried out genetic algorithm, and by the quantum genetic searching algorithm being applied to the value that described genetic algorithm is calculated, derive described final instructional signal (443), objective function depend on described interactive information value (I1, I2).

12. according to Claim 8 to one of 11 method, wherein said to want minimized physical quantity (s) be the entropy production of described control procedure (488).

13. according to Claim 8 to one of 11 method, wherein

Described control procedure (488) is an internal combustion engine,

At least one of described first and second groups of sensors comprise that at least one belongs to the sensor of the sensor groups of being made up of crank angle sensor, pressure transducer and cooling-water temperature sensor.

Described the 3rd group of sensor comprises an air oil ratio sensor at least.

14. according to Claim 8 to one of 11 method, wherein

Described control procedure (488) is the suspension vehicle,

At least one group of described sensor comprises that at least one belongs to the sensor of the sensor groups of being made up of position transducer, slant angle sensor and roll angle sensor.

Images