CN106406087A - Intelligent control system optimization algorithm based on transformation function and filled function - Google Patents

Abstract

The invention discloses an intelligent control system optimization algorithm based on a transformation function and a filled function. The method comprises the following steps: (1) initializing parameters; (2) judging whether to end an algorithm process: k>MN or L>TT; (3) judging whether to enter a filled function: abs(gi(x)-fi(x))<d1, k<=FMN, and fi(x) >=f_allbest; if the conditions are met, entering the filled function, updating an independent variable Xnxd and the values f(X)=[f1, f2...fn] of n subsystems of an objective function after T transformation and going back to step (3); if the conditions are not all met, jumping to step (4); (4) updating the parameters; (5) updating related error terms E, delta(E) and delta<2>(E), adjusting an inertial factor w as well as the parameters ki, kp and kd of a PID algorithm, and jumping to step (2). The innovation of the invention lies in that a transformation function method and a filled function method are adopted in a multi-loop feedback intelligent control system to realize optimization, so that the possibility that the algorithm gets into local optimum is reduced, and the optimization precision and speed are increased.

Description

Intelligence control system optimized algorithm based on transforming function transformation function and stuffing function

Technical field

The present invention proposes a kind of intelligence control system optimized algorithm based on transforming function transformation function and stuffing function, wherein intelligently Control system is multiloop feedback control system, and it makes the control object of each sub-loop is optimised function, by each The feedback of sub-loop and the distribution of many sub-loops, realize control object optimization；Transforming function transformation function simplifies object function, so that it is complete Office's smallest point is separated with other local minimums；Stuffing function has makes intelligence control system jump to separately from local best points The function of one less local best points, so can obtain more accurate globe optimum repeatedly several times.

Background technology

The basic ideas of feedback control system optimized algorithm derive from the feedback thought of single loop control system, specific frame Graph model is illustrated in fig. 5 shown below.Wherein, input set-point R is usually a constant being less than object function minimum of a value；From Fig. 5 not It is difficult to see, feedback control system is mainly passed through output feedback and produced error, controls controlled device (optimised letter through controller Number), thus realizing optimizing, that is, the optimised function as control object passes through feedback so that it is exported less and less with controller.

In Figure 5, f (k) is target function value during kth time iteration；Controller adopt incremental timestamp strategy, single time The iterative formula of road feedback control system optimized algorithm is defined as：

X (k+1)=x (k)+k_pΔE(k)+k_iE(k)+k_dΔ²E(k) (1)

K in above formula_p, k_iAnd k_dIt is tri- self-adaptative adjustment parameters of PID respectively.

The function to some complicated Multi-maximum point for this algorithm, after sometimes up to certain precision, is difficult to find more again Good extreme point, or it is unable to reach target call, for this reason, certain transforming function transformation function is used for simplifying object function (control object) It is allowed to become simple convex function as much as possible.When the value of object function is away from zero, its value is mapped to 1 or -1, and works as mesh The value of scalar functions close to zero when, then its value is mapped to zero as far as possible.Further, since transfer function changes very near zero Greatly, therefore, by functional transformation, the global minima point of object function and other local minimums minute near zero point can be made From.In conjunction with the intelligence control system with the control object being simplified, we can obtain the more accurately complete of object function Office's smallest point.

If function T (x) meets following two properties, the function that we are just called object function f (x) it becomes Change：

1) T (x) (wherein x ＞ 0) is the continuous, one-dimensional functions that can lead and is dull on (0,1) or (- 1,0) 's.

2) | (T (± 10)-T (0)) |/T (∞) >=98%

Note 1：Property 1 ensure that function T (x) after conversion and object function f (x) have identical globe optimum.Property Matter 2 is to provide the valid interval of T (x).

This algorithm faces the test of two problems.First problem is：How to judge current minimum point be the overall situation Figure of merit point；Second Problem is：How to jump out from current local minimum point, shift to the less local minizing point of object function.

Filled Function Methods are a kind of methods that can preferably solve to be absorbed in local minimum point, can be had by constructing stuffing function Jump out local minimum point to effect, find another local minimum point less than it.In order to more fully understand stuffing function, below Provide three hypothesis.

Assume 1：One of function f (x) comprises smallest pointConnected domain B₁, set out in its internal any point x, with speed Fall method all converges onBut B₁The part arbitrfary point of outside all can not converge onThen B₁It is called a basin domain of f (X).

Assume 2：IfIt is the maximum point of f (x), then f (x) comprisesPaddy domain be-f (x) basin domain.

Assume 3：Comprise local minimum pointBasin domain B₂It is above comprising local minimumBasin domain B₁And if only if

If function P (x, an x^*) meeting following four condition, then it is known as f (x) in local minimum point's Stuffing function：

1)It is function P (x, x^*) a strict local maximum point.

2) at any one higher than bath in a tub B₁F (x) bath in a tub, P (x, x^*) there is no smallest point or saddle point.

3) if f (x) has one in local minimum pointsThan basin domain B₁Little basin domain B₂, then exist 1 point of x ' make P (x, x^*) minimum, and itWith x " connecting line on (it isSome neighborhood).

4) for any x, the y belonging to Ω domain, meet WithAnd if only if P (x)≤(＜) P (y).

Content of the invention

Present invention aims to the deficiency that prior art exists, one kind is provided to be based on transforming function transformation function and stuffing function Intelligence control system optimized algorithm, its intelligence control system is multiloop feedback control system, and it makes each sub-loop Control object is optimised function, by the feedback of each sub-loop and the distribution of many sub-loops, realizes control object optimization.Cause The majorized function of Multi-maximum point is easily absorbed in Local Extremum, introduces transforming function transformation function simplify control object, makes optimised function Global minima point can be separated with other local minimums near zero point.Transforming function transformation function is dull one-dimensional functions, does not affect mesh The number of the extreme point of scalar functions.Control system is made to jump out current Local Minimum based on the stuffing function of optimised construction of function Point, and can restart to find the local minimum points less than current minimum of a value in new position, thus avoiding making system fall into Enter local minimum points.

For reaching above-mentioned purpose, idea of the invention is that：Intelligence control system adopts multiloop feedback control system, each The control object of individual sub-loop is optimised function, carries out T conversion using transforming function transformation function to control object, makes optimised function Global minima point (close to the minimum of a value of zero point) can separate with other local minimums near zero points, use self-adaptive PID The optimal value of optimised function found by controller.(the quilt after adjacent iteration twice when being judged as being absorbed in local minimum During the difference very little of majorized function value), now enter stuffing function iteration, until jump out local minimum and find one less Smallest point, continues to use self-adaptive PID controller searching system optimal value on this basis.

Conceived according to foregoing invention, the present invention adopts following technical proposals：

The first step：Parameters are initialized：Determine initial point X using random distribution in feasible zone_n×dJust Value, wherein n is concurrent control system number, and d is the dimension of actual argument, to parameters local minimum points x_{_best}, the overall situation Smallest point x_{_allbest}, local minimum f_{_best}, global minimum f_{_allbest}, inertial factor w, parameter k of pid algorithm_i, k_p, k_d, [0,2] the constant c between₁, c₂, random number r₁, r₂Interval initial value, and determine algorithm global cycle number of times MN, enter stuffing function Maximum times TT of subprogram and maximum times ND of stuffing function inner iteration, make k=1, L=1.m=1；

Second step：Judge whether to terminate algorithm flow：k>MN or L>TT, if so, then exports the global optimum of object function Value f_{_allbest}, EP (end of program)；Otherwise, k=k+1, g_i(x)=f_i(x), i=1,2,3...n；Updated certainly according to following formula (3) Variable X_n×dValue f (X)=[f with the n subsystem of object function after T conversion₁,f₂...f_n] and judge vector x whether beyond can Row domain；

3rd step：Judge whether to enter stuffing function:abs(g_i(x)-f_i(x)) ＜ d₁And m≤ND and f_i(x)≥f_ Allbest, if so, then x (i, k)=x (i, k)+d₂×(rand(1,1)-0.5)×exp(d₃(k-1)/ND)

X (i, k)=x (i, k)+d₄×rand(1,1)×exp(d₅(k-1)/ND)×(x(i,k)-x_allbest)/||x (i, k)-x_allbest | | enter stuffing function, update f (x), T conversion after n subsystem of object function value f (X)= [f₁,f₂...f_n],g_i(x)=f_i(x), i=1,2,3...n, then go back to the 3rd step；Otherwise, jump to the 4th step；

4th step：Update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}；

5th step：Correlated error amount E, Δ E, Δ are updated according to formula (4)²E.Inertial factor w is adjusted according to formula (5), PID calculates Parameter k of method_i, k_p, k_d, then jump to second step.

In above-mentioned second step, object function f (x) is carried out with the concrete grammar of T conversion：The T of object function f (x) is transformed toHere T transforming function transformation function isUpdate independent variable X_n×dIterative equation formula be：

Wherein x (i, k) represents iterative vectorized, the k of kth time of i-th subsystem_i, k_p, k_dIt is the parameter vector of pid algorithm, w It is inertial factor.r₁, r₂It is the interval random number of initial value design.c₁, c₂It is constant, general span is [0,2].x_best I () is i-th subsystem desired positions vector in an iterative process, x_allbest be all systems in iterative process Good position vector.Judge whether vector x exceeds feasible zone：X ＜ s₁Or x ＞ s₂, if so, then exceed feasible zone, x (i, k+1)= x_{_allbest}K (), updates f (X)=[f₁,f₂...f_n]；Otherwise, without departing from feasible zone, with this iteration result x (i, k+1) more New f (X)=[f₁,f₂...f_n], wherein k is used for adding up algorithm cycle-index, and g (x) is used for preserving the value of this f (x), and MN is to calculate The maximum of method cycle-index；L is used for the accumulative number of times entering stuffing function subprogram, and TT allows access into stuffing function subprogram Maximum times；s₁, s₂Border for independent variable x valid interval.

In above-mentioned 3rd step, judge whether to enter stuffing function, its Rule of judgment is：abs(g_i(x)-f_i(x)) ＜ d₁And m ≤ ND and f_iX () >=f_allbest, m are used for being accumulated at the number of times of stuffing function inner iteration, ND is in stuffing function inner iteration Maximum times, d₁For being set into the maximum of the absolute value of the difference of the adjacent f (x) twice during stuffing function subprogram.

2., in above-mentioned 4th step, update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}：If f (i, k+1) ＜ f_{_best}(i), then x_{_best}(i)=x (i, k+1), f_{_best}(i)=f (i, k+1)；If f_{_allbest}(k) ＞ f_{_best}(i, k+1), then x_{_allbest}(k)= x_{_best}(i, k+1), f_{_allbest}(k)=f_{_best}(i, k+1) otherwise jumps to step 5).

In above-mentioned 5th step, correlated error amount E, Δ E, Δ²The more new formula of E and parameter ω, k_p、k_iAnd k_dSelf adaptation Correction formula is as follows：

η is a very little positive number, and R is system input, and f (i, k) represents the kth subsystem output f of i-th subsystem The value of (x).Δ E (i, k) represents kth secondary system error E (i, k) and kth -1 secondary system error E (i, k-1) of i-th subsystem Difference, Δ²E (i, k) represents kth secondary system error E (i, k) and kth -1 secondary system error E (i, k-1) of i-th subsystem The difference of kth -1 secondary system error E (i, k-1) and kth -2 secondary system error E (i, k-2) of difference and i-th subsystem Difference.

The transforming function transformation function used in the present invention：Function T (x) can be clearly seen former from Fig. 7 Value changes near point are very big and domain of definition is interior very gentle away from the regional change of initial point, the new mesh that this explanation is obtained by conversion Scalar functions are cut in the local minimum away from initial point, and the global minimum in initial point vicinity is exaggerated, thus The system of reducing is absorbed in the possibility of local minimum points.In order to verify this point, take an example F1, transforming function transformation function T (x) is processed Curve in front and back is as shown in Fig. 8～9.

The present invention proposes a kind of stuffing function without parameter and provides proof：

Theorem 1：If x₁Known local minimum points of f (x), then x₁It is P (x, x₁) a strict local Maximum point.Prove：If B₁It is f (x) in local minimum points x₁A s type basin domain, that is, to any x ∈ B₁There is f (x) >=f (X₁), Then

This shows x₁It is P (x, x₁) a strict local maximum point.

Theorem 2：Make x₁It is known local minimum points of f (x), if x is ∈ S₁=x | f (x) >=f (X₁),x≠ X₁, then P (x, x₁) in S₁Fixed point free or smallest point in domain.

Prove：Because x is ∈ S₁,Then as f (x) ＞ f (X₁) and x ≠ X₁, haveIf d (x)=(x-x₁) and x ≠ X₁, thenTherefore d (x) is for any x ∈ S₁, P (x, x₁) a prompt drop direction.When F (y)=f (X₁), haveThen for satisfaction || x-x₁|| ＞ || y-x₁|| and || x₂-x₁|| ＜ | | y-x₁| | any x, x₂∈S₁, have Therefore, P (x, x₁) in S₁Fixed point free or smallest point in domain.

Theorem 3：Make x₁It is known local minimum points of f (x), for any x₂∈Ω,x₂≠x₁If, f (x₂) ≥f(x₁), then x₂It is P (x, x₁) a continuity point, or x₂It is P (x, x₁) a hollow grassland point.

Prove：Because x₁It is the B of f (x)₁Local minimum points in basin domain, so for any x ∈ B₁, have f (x) >= f(x₁), thenTherefore, P (x, x₁) in x₁Point is continuous.As Fruit f (x₂)≠f(x₁) and x₂≠x₁, i.e. f (x₂) ＜ f (x₁) or f (x₂) ＞ f (x₁), thenOrSo there is a neighborhood N (x₂, δ), δ ＞ 0 makes for any x ∈ N (x₂, δ),I.e. P (x, x₁) in x₂Point is continuous.If f is (x₂)=f (x₁) and x₂≠x₁, thenTherefore x₂It is P (x, x₁) a hollow grassland point.

Theorem 4：Make x₁It is known local minimum points of f (x), x₂It is to meet f (x₂) ＜ f (x₁) another and x₁ , then there is 1 point of x' ∈ S in neighbouring local minimum points₂={ x, f (x) ＜ f (X₁), x ∈ Ω } make P (x, x^*) minimum, and itWith x " connecting line on (it isSome neighborhood).

Prove：Because x₁It is known local minimum points of f (x), then there is a s type basin domain B₁, for any x ∈B₁, make f (x) >=f (x₁), thus obtain

Similarly, with regard to local minimum points x₂, there is s type basin domain B₂, for some x₃∈B₂, have f (x₂)≤f(x₃) ＜ f (x₁), then for x₃∈B₂, have

Therefore P (x', x₁)<P(x₃,x₁), in addition P (x₁,x₁)=0, then when x is away from x₁When, there are P (x, x₁) ＜ 0.Therefore, As f (x) >=f (x₁) when, P (x, x₁) reduce, otherwise P (x, x₁) increase.By theorem 4, then there is 1 point of x' ∈ S₂={ x, f (x) ＜ f (X₁), x ∈ Ω } make P (x, x^*) minimum, and itWith x " connecting line on (it isSome neighborhood).

Theorem 5:Make x₁It is known local minimum points of f (x), and d is to meet d^T(x-X₁) ＞ 0 a side To if f (x) is ＞ f (X₁), then d is P (x, x₁) in x₁One prompt drop direction of point.

Prove：Because f (x) is ＞ f (X₁) and d^T(x-X₁) ＞ 0, then

Therefore d It is P (x, x₁) in x₁One prompt drop direction of point.

Theorem 6：Make x₁It is known local minimum points of f (x), for any x, y ∈ Ω meets

f(x)≥f(X₁),f(y)≥f(X₁) and | | x-x₁||≥||y-x₁| | and if only if P (x, x₁)≤P(y,x₁).

Prove：Because for any x, y ∈ Ω meets f (x) >=f (X₁),f(y)≥f(X₁), then

BecauseMonotonically increasing function, then for | | x-x₁| | ＞ (>=) || y-x₁||, there are P (x, x₁) ＜ (≤) P(y,x₁) or for P (x, x₁) ＜ (≤) P (y, x₁), have || x-x₁|| ＞ (>=) || y-x₁||.

Note 1：From theorem 16, it is readily seen P (x, x₁) it is a stuffing function, because it meets stuffing function All of definition, as f (x) >=f (x₁), P (x, x₁) reduce；As f (x) ＜ f (x₁), P (x, x₁) increase, if d is in a satisfaction d^T(x-X₁) ＞ 0 P (x, x₁) prompt drop direction, then can find by d meeting f (x) ＜ f (x₁) the direction of search.

OrderIt is current local minimum point,It is current iteration point, λ and μ is two given constants and 0 ＜ λ ＜ μ, BeThe direction of search, make

Theorem 7:OrderWithIfMeetThen

Here, Ω is the feasible zone of x.

Prove：IfThen

Note 2：From theorem 3 it is easy to see, ifIt is a satisfactionThe direction of search, So when iterations reaches sufficiently large, search is up to the border of Ω or finds and meet f (x) ＜ f (X₁) point.In order to Realize

WithWe select? It is exactly

Say,ThereforeThis In, η ＞ 0.When border Ω is very big, η can elect a larger positive number as, otherwise η can elect as one less Positive number.In addition, in order to avoid search reach border it is necessary to using distributivity Learning Step, therefore η can elect as one with The positive number of machine.

Obtain the thinking based on stuffing function algorithm from the definition of stuffing function, calculate first by a kind of local optimum Method obtains a local minimum point of object function f (X)Then existPlace's one stuffing function F (x) of construction,Place's search 1 point of x₁, with x₁For starting point Local Optimization Algorithm minimization stuffing function F (x), obtain 1 point of x₂, have the property of stuffing function Matter understands, point x₂One is scheduled on and compares B₁In low basin domain, then from now acquired minimal point x₂For initial point local optimization methods Minimization object function f (X), obtains another more excellent local minimum point of f (X)Alternately said process will obtain Local minimum point range profit to object function f (X)X*, meetsThus Global minimum to object function.

The intelligence control system optimized algorithm based on transforming function transformation function and stuffing function of the present invention is compared with prior art Have and obviously project substantive distinguishing features and remarkable advantage as follows：

1) intelligence control system is multiloop feedback control system, it make each sub-loop control object be optimised Function, by each sub-loop feedback and many sub-loops distribution, realize control object optimization.

2) optimised function is simplified by functional transformation so as to be cut in and former in the local minimum away from far point Local minimum near point is exaggerated, thus reducing the possibility being absorbed in local minimum points, largely increases Find the possibility of global minimum, improve the accuracy and speed of optimizing.

3) when system has been absorbed in local best points, enter stuffing function iteration, make intelligence control system from a local Optimum point jumps to another less local best points, so repeatedly can obtain more accurate globe optimum several times.

4) the intelligence control system and function conversion of multiloop system parallel computation and the combination of Filled Function Methods, both protected The advantage having stayed the multisystem distributed parallel computing of intelligence control system, and overcome intelligence control system calculation to a certain extent Method is easily trapped into the deficiency of local best points.

Brief description

Fig. 1 algorithm main flow chart；

Fig. 2 algorithm sub-process figure；

Fig. 3 algorithm sub-process figure；

Fig. 4 algorithm sub-process figure；

The model of Fig. 5 single loop feedback control system optimized algorithm

The multiloop system block diagram based on transforming function transformation function and stuffing function for the Fig. 6；

Fig. 7 is the curve of transforming function transformation function T (x)；

Fig. 8 is the curve of F1 (x), domain of definition (- 6<x<6)；

F1 (x) after Fig. 9 T conversion is the curve of T (F1 (x)), domain of definition (- 6<x<6)；

The simulation curve to 5 algorithms of F1 reference function for the Figure 10；

The simulation curve to 5 algorithms of F2 reference function for the Figure 11；

The simulation curve to 5 algorithms of F3 reference function for the Figure 12；

The simulation curve to 5 algorithms of F4 reference function for the Figure 13；

The simulation curve to 5 algorithms of F5 reference function for the Figure 14；

Specific embodiment

It is as follows that the preferred embodiments of the present invention combine detailed description：

Embodiment one：

Reference function：

Hunting zone：-5.12≤x_i≤ 5.12 (experiment herein is using 30 dimensions).Global optimum：Min (F1)=F1 (0 ..., 0)=0.Referring to Fig. 1～Fig. 9, this intelligence control system optimized algorithm based on transforming function transformation function and stuffing function, it is special Levy and be that operating procedure is as follows：

1) parameters are initialized：Determine initial point X using random distribution in feasible zone_5×30=10.24 × (rand (5,30,1) -0.5), wherein 5 is concurrent control system number, and 30 is the dimension of actual argument, local minimum points x_{_best}=10.24 × (rand (5,30,1) -0.5), global minima point x_{_allbest}=0 × rand (1,30,1), local minimum f_{_best}=2 × 10⁸× rand (5,1,1), global minimum f_{_allbest}=2 × 10⁷, inertial factor w=0.01 × rand (5, 30,1), parameter k of pid algorithm_i=k_d=1 × 10^-8× rand (5,30,1), k_p=5 × 10^-8× rand (5,30,1), c₁= c₂=1.5, r₁=r₂=1.0 × (rand (1,1) -0.5), algorithm global cycle number of times MN=40, enter stuffing function subprogram Maximum times TT=80, and maximum times ND=300 of stuffing function inner iteration, d₁=1 × 10^-15,d₁=1 × 10^-7,d₃= 5,d₄=1, d₅=3, k=1, L=1, m=1；

2) judge whether to terminate algorithm flow：k>40 or L>80, if so, then export the global optimum of object function f_{_allbest}, EP (end of program)；Otherwise, k=k+1, g_i(x)=f_i(x), i=1,2,3,4,5；Update independent variable X_5×30After T conversion 5 subsystems of object function value f (X)=[f₁,f₂...f₅] and judge whether vector x exceeds feasible zone；

3) judge whether to enter stuffing function：abs(g_i(x)-f_i(x)) ＜ 1 × 10^-15And m≤300 and f_i(x)≥f_ Allbest, if so, then x (i, k)=x (i, k)+1 × 10^-7×(rand(1,1)-0.5)×exp(5×(k-1)/300)

X (i, k)=x (i, k)+1 × rand (1,1) × exp (3 × (k-1)/300) × (x (i, k)-x_allbest)/| | X (i, k)-x_allbest | | enter stuffing function, update f (x), T conversion after 5 subsystems of object function value f (X)= [f₁,f₂...f₅],g_i(x)=f_i(x), i=1,2,3,4,5, then go back to step 3)；Otherwise, jump to step 4)；

4) update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}；

5) correlated error amount E, Δ E, Δ are updated²E；Adjustment inertial factor w, parameter k of pid algorithm_i, k_p, k_d, then jump Go to step 2).

Embodiment two：

The present embodiment is essentially identical with embodiment one, is particular in that as follows：

Described operating procedure 2) in, object function f (x) is carried out with the concrete grammar of T conversion：The T of object function f (x) becomes It is changed toHere T transforming function transformation function isUpdate independent variable X_n×dIterative equation Formula is：

Wherein x (i, k) represents that the kth time of i-th subsystem is iterative vectorized, and x_best (i) is i-th subsystem in iteration During desired positions vector, x_allbest is all systems in the desired positions vector of iterative process；Judge x (i, k+1) Whether exceed feasible zone：X ＜ -5.12 or x ＞ 5.12, if so, then exceeds feasible zone, x (i, k+1)=x_{_allbest}K (), updates f (X)=[f₁,f₂...f₅]；Otherwise, without departing from feasible zone, f (X)=[f is updated with this iteration result x (i, k+1)₁, f₂...f₅].

Described operating procedure 3) judge whether to enter stuffing function：Rule of judgment is abs (g_i(x)-f_i(x)) ＜ 1 × 10^-15 And m≤300 and f_i(x) >=f_allbest, if so, then x (i, k)=x (i, k)+1 × 10^-7×(rand(1,1)-0.5)×exp (5×(k-1)/300)

X (i, k)=x (i, k)+1 × rand (1,1) × exp (3 × (k-1)/300) × (x (i, k)-x_allbest)/| | X (i, k)-x_allbest | | enter stuffing function, see if fall out feasible zone, then update f (X)=[f₁,f₂...f₅], T conversion is carried out to f (x).

Described operating procedure 4) update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}：If f (i, k+1) ＜ f_{_best}(i), then x_{_best}(i)=x (i, k+1), f_{_best}(i)=f (i, k+1)；If f_{_allbest}(k) ＞ f_{_best}(i, k+1), then x_{_allbest}(k)= x_{_best}(i, k+1), f_{_allbest}(k)=f_{_best}(i, k+1) otherwise jumps to step 5).

Described operating procedure 5), correlated error amount E, Δ E, Δ²The more new formula of E and parameter ω, k_p、k_iAnd k_dAdaptive Answer correction formula as follows：

Here η=1 × 10^-11, system input R=-20, initialization f (X)=0 × rand (5,1,1).

Embodiment three：

Fig. 1 is algorithm main flow chart, by Fig. 1, F1 is initialized first, then judges whether to terminate algorithm, if not tying Bundle algorithm is pressed Fig. 2 and is updated independent variable X, judges whether X exceeds feasible zone, updates f (x)；Then judge whether to enter filling by Fig. 3 Function, judges whether X exceeds feasible zone, updates f (x), carries out T conversion to f (x)；Then press Fig. 4 and update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}；Then press Fig. 1 and update correlated error amount E, Δ E, Δ²The more new formula of E and parameter ω, k_p、k_iAnd k_d, circulation Repeatedly above-mentioned steps.Based on single loop feedback control system classical shown in Fig. 5, the present invention adopts shown in Fig. 6 based on filling The multiloop feedback control system of function.Fig. 7 is the transforming function transformation function used in algorithmFigure.Fig. 8 isFigure, as can be seen from Fig., F1 has a lot of local minimum points, be not easy to find letter The global minima point of number.Fig. 9 be to F1 conversion afterFigure, transformed rear globally optimal solution is very Prominent, and the local minimum point at edge is weakened, so that global optimizing is become easier to, more precisely.

Figure 10 to Figure 14 is the simulation result that function is made on the basis of F1～F5.In figure curve 1 is APID algorithm (parameter Self-adaptive PID feedback control system optimized algorithm), curve 2 is that (parameter adaptive multiloop PID/feedback controls system to MAPID algorithm System optimized algorithm), curve 3 is that TAPID algorithm (calculate by the self-adaptive parameter PI D feedback control system optimization based on transforming function transformation function Method), curve 4 is TMAPID algorithm (the parameter adaptive multiloop PID/feedback control system optimized algorithm based on transforming function transformation function), Curve 5 is that (the parameter adaptive multiloop PID/feedback control system based on transforming function transformation function and stuffing function is excellent for FTMAPID algorithm Change algorithm, the algorithm that is, present invention discusses).Abscissa is algorithm iteration number of times, and ordinate is the functional value of f (x).From Figure 10 to Figure 14 can find out that the precision of the control system optimized algorithm convergence wherein based on transforming function transformation function and stuffing function can obtain further Improve, it is more preferable that the speed of convergence also becomes.

Here each test function is repeated to test 30 times, count the maximum (MAX) in 30 times, minimum of a value (MIN), become The mean value (AVG) of work(convergence, confidential interval (Confidence Interval, according to 95% confidence level), convergence times N And the CPU time (CPU-TIME).Finally in order to more intuitively describe the problem, give the imitative of four algorithms in same width in figure True curve carries out Performance comparision to facilitate.In experiment, allowable error is SA, i.e. simulation result and reality in setting iterative steps Error between optimal value is then considered successfully to restrain less than SA, does not otherwise restrain (being represented with "/").

The experimental result of table 1 F1Generalized Griewanks function

The experimental result of table 2 F2Goldstein-Price function

The experimental result of table 3 F3Shubert function

The experimental result of table 4 F4Shekel ' s Family function

The experimental result of table 5 F5weierstrassy function

Data from table 1 to table 5 can be seen that relative with the control system optimized algorithm of stuffing function based on transforming function transformation function In above four kinds of control algolithms, decrease the possibility that algorithm is absorbed in optimal value, complete successfully convergence and convergence precision is all fine.

The intelligence control system of multisystem parallel computation be combined with Filled Function Methods based on transforming function transformation function and stuffing function Control system optimized algorithm, on the one hand, both remained the multisystem parallel computation of intelligence control system and the excellent of team learning Point, and overcome the deficiency that intelligence control system algorithm is easily trapped into local best points to a certain extent.On the other hand, intelligence Control system algorithm has stronger local search ability, and stuffing function rule ensure that the overall situation of intelligence control system algorithm Search, thus substantially increase the low optimization accuracy of intelligence control system algorithm.

It is given below corresponding to Figure 10 to Figure 14, as 5 benchmark test functions of optimised function：

1.Generalized Rastrigin function

Function expression：

Hunting zone：-5.12≤x_i≤ 5.12 (experiment herein is using 30 dimensions).

Global optimum：Min (F1)=F1 (0 ..., 0)=0.

2.Kowalik function

Function expression：

Hunting zone：-2≤x_i≤ 2 (independent variable 4 is tieed up).

Global optimum：min(F2)≈F2(-0.1928,0.1908,0.1231,0.1358)≈3.0749e-4

3.Shubert function

Function expression：

Hunting zone：-10≤x_i≤ 10 (independent variable 2 is tieed up).Global optimum：Min (F3)=- 186.7309.

4.Shekel’s Family

Function expression：

C=[0.1 0.2 0.2 0.4 0.4 0.6 0.3 0.7 0.5 0.5]

Hunting zone：0≤x_i≤ 10 (independent variable 4 is tieed up).Global optimum：Min (F4)=F4 (4,4,4,4)=- 10.5364.

5.Weierstrass function

Function expression：

A=0.5, b=3, kmax=20

Hunting zone：-5.12≤x_i≤ 5.12 (experiment herein is using 10 dimensions).Global optimum：Min (F5)=F5 (0 ... 0)=0.

Claims (5)

1. a kind of intelligence control system optimized algorithm based on transforming function transformation function and stuffing function it is characterised in that operating procedure such as Under：

1) parameters are initialized：Determine initial point X using random distribution in feasible zone_n×dInitial value, wherein n is Concurrent control system number, d is the dimension of actual argument, to parameters local minimum points x_{_best}, global minima point x_{_allbest}, local minimum f_{_best}, global minimum f_{_allbest}, inertial factor w, parameter k of pid algorithm_i, k_p, k_d, [0,2] Between constant c₁, c₂, random number r₁, r₂Interval initial value, and determine algorithm global cycle number of times MN, enter the sub- journey of stuffing function Maximum times TT of sequence and maximum times ND of stuffing function inner iteration, given d₁,d₂,d₃,d₄,d₅. make k=1, L=1, m= 1；

2) judge whether to terminate algorithm flow：k>MN or L>TT, if so, then exports global optimum f of object function_{_allbest}, EP (end of program)；Otherwise, k=k+1, g_i(x)=f_i(x), i=1,2,3...n；Update independent variable X_n×dWith the target letter after T conversion Value f (X)=[f of n subsystem of number₁,f₂...f_n] and judge whether vector x exceeds feasible zone；

3) judge whether to enter stuffing function：abs(g_i(x)-f_i(x)) ＜ d₁And m≤ND and f_i(x) >=f_allbest, if so, Then x (i, k)=x (i, k)+d₂×(rand(1,1)-0.5)×exp(d₃(k-1)/ND) x (i, k)=x (i, k)+d₄×rand (1,1)×exp(d₅(k-1)/ND) × (x (i, k)-x_allbest)/| | x (i, k)-x_allbest | | entrance stuffing function, Update f (x), value f (X)=[f of the n subsystem of object function after T conversion₁,f₂...f_n],g_i(x)=f_i(x), i=1,2, 3...n, then go back to step 3)；Otherwise, jump to step 4)；

4) update x_{_best}, x_{_allbest}, f_{_best}, f_{_allbest}；

5) correlated error amount E, Δ E, Δ are updated²E；Adjustment inertial factor w, parameter k of pid algorithm_i, k_p, k_d, then jump to step Rapid 2).

2. the intelligence control system optimized algorithm based on transforming function transformation function and stuffing function according to claim 1, its feature It is：Described operating procedure 2) in, object function f (x) is carried out with the concrete grammar of T conversion：The T of object function f (x) is transformed toHere T transforming function transformation function isUpdate independent variable X_n×dIterative equation formula be：

$\begin{array}{c}x(i,k+1)=w\left(i\right)\&CenterDot;x(i,k)+k_p\left(i\right)\&CenterDot;\mathrm{\&Delta;}E(i,k)+k_i\left(i\right)\&CenterDot;E(i,j)+\\ k_d\left(i\right)\&CenterDot;{\mathrm{\&Delta;}}^{2}E\left(i,k\right)+r_1\left(i\right)\&CenterDot;c_1\left(i\right)\&CenterDot;\left(x\_best\left(i\right)-x\left(i,k\right)\right)+\\ r_2\left(i\right)\&CenterDot;c_2\left(i\right)\&CenterDot;\left(x\_allbest-x\left(i,k\right)\right)\end{array}---\left(1\right)$

Wherein x (i, k) represents iterative vectorized, the k of kth time of i-th subsystem_i, k_p, k_dIt is the parameter vector of pid algorithm, w is used Sex factor；r₁, r₂It is the interval random number of initial value design；c₁, c₂It is constant, general span is [0,2]；X_best (i) is I-th subsystem desired positions vector in an iterative process, x_allbest is the desired positions in iterative process for all systems Vector；Judge whether x (i, k+1) exceeds feasible zone：X ＜ s₁Or x ＞ s₂, if so, then exceed feasible zone, x (i, k+1)= x_{_allbest}K (), updates f (X)=[f₁,f₂...f_n]；Otherwise, without departing from feasible zone, with this iteration result x (i, k+1) more New f (X)=[f₁,f₂...f_n], wherein k is used for adding up algorithm cycle-index, and g (x) is used for preserving the value of this f (x), and MN is to calculate The maximum of method cycle-index；L is used for the accumulative number of times entering stuffing function subprogram, and TT allows access into stuffing function subprogram Maximum times；s₁, s₂Border for independent variable x valid interval.

3. the intelligence control system optimized algorithm based on transforming function transformation function and stuffing function according to claim 1, its feature It is：Described operating procedure 3) judge whether to enter stuffing function, wherein Rule of judgment is：abs(g_i(x)-f_i(x)) ＜ d₁And m ≤ ND and f_iX () >=f_allbest, m are used for being accumulated at the number of times of stuffing function inner iteration, ND is in stuffing function inner iteration Maximum times, d₁For being set into the maximum of the absolute value of the difference of the adjacent f (x) twice during stuffing function subprogram.

4. the intelligence control system optimized algorithm based on transforming function transformation function and stuffing function according to claim 1, its feature It is：Described operating procedure 4) update x_{_best}, x_{_allbest}, f_{_best}And f_{_allbest}：If f (i, k+1) ＜ f_{_best}(i), then x_{_best}(i)=x (i, k+1), f_{_best}(i)=f (i, k+1)；If f_{_allbest}(k) ＞ f_{_best}(i, k+1), then x_{_allbest}(k)= x_{_best}(i, k+1), f_{_allbest}(k)=f_{_best}(i, k+1) otherwise jumps to step 5).

5. the intelligence control system optimized algorithm based on transforming function transformation function and stuffing function according to claim 1, its feature It is：Described operating procedure 5), correlated error amount E, Δ E, Δ²The more new formula of E and parameter ω, k_p、k_iAnd k_dSelf adaptation repair Positive formula is as follows：

$\left\{\begin{array}{c}E(i,k)=R-f(i,k-1)\\ \mathrm{\&Delta;}E(i,k)=E\left(i,k\right)-E(i,k-1)\\ {\mathrm{\&Delta;}}^{2}E(i,k)=E(i,k)-2\&CenterDot;E(i,k-1)+E(i,k-2)\end{array}\right.---\left(2\right)$

$\left\{\begin{array}{c}\mathrm{\&omega;}(i,k+1)=\mathrm{\&omega;}(i,k)-\mathrm{\&eta;}\&CenterDot;\frac{\&part;f\left(x\right)}{\&part;x}\&CenterDot;x(i,k)\\ k_p(i,k+1)=k_p(i,k)-\mathrm{\&eta;}\&CenterDot;\frac{\&part;f\left(x\right)}{\&part;x}\&CenterDot;\mathrm{\&Delta;}E(i,k)\\ k_i(i,k+1)=k_i(i,k)-\mathrm{\&eta;}\&CenterDot;\frac{\&part;f\left(x\right)}{\&part;x}\&CenterDot;E(i,k)\\ k_d(i,k+1)=k_d(i,k)-\mathrm{\&eta;}\&CenterDot;\frac{\&part;f\left(x\right)}{\&part;x}\&CenterDot;{\mathrm{\&Delta;}}^{2}E(i,k)\end{array}\right.---\left(3\right)$

Here η is a very little positive number, and R is system input, and f (i, k) represents the kth subsystem output f of i-th subsystem The value of (x).Δ E (i, k) represents kth secondary system error E (i, k) and kth -1 secondary system error E (i, k-1) of i-th subsystem Difference, Δ²E (i, k) represents kth secondary system error E (i, k) and kth -1 secondary system error E (i, k-1) of i-th subsystem The difference of kth -1 secondary system error E (i, k-1) and kth -2 secondary system error E (i, k-2) of difference and i-th subsystem Difference.