CN105629733B - A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method - Google Patents
A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method Download PDFInfo
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Abstract
A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method, by selecting fractional order differential algorithm, the equation definition of combination cell neural network, constructs a three-dimensional fractional order dynamic stability.Designed in the system-based known to a drive system nonlinear parameter and the unknown driving response system of response system nonlinear parameter, a new Adaptive synchronization controller and parameter adaptive regulation are constructed at the same time, and driving and the synchronization of response system are realized in numerical simulation；Fractional order cell neural network drive system and response system circuit diagram are designed, while circuit simulation is realized to controller and adaptive regulation.Simulation result of the present invention shows that circuit simulation has similar synchronous phasor with numerical simulation, demonstrates the realizability in the correctness and actual physics of Systems Theory analysis, the application value in engineering field with reality.
Description
Technical field
The invention belongs to non-thread line chaotic circuit system field, is related to cell neural network, Synchronization Control theory and fraction
Rank circuit thought.
Background technology
Chaos was the discovery that for 20th century after one of greatest discovery, chaos in physics after the theory of relativity and quantum mechanics
Movement is a kind of exclusive forms of motion of deterministic nonlinear system, show as being seen as finite motion from global scope and from
Local angle sees to be then irregular movement.The characteristics of chaos is its extreme sensitivity to disturbance, i.e. two chaos systems from
The primary condition of minute differences is set out, and by regular hour meeting rapid divergence, it is entirely different to ultimately result in movement locus.Exactly
Due to the height random, unpredictability, high complexity of chaotic signal, and the being easily achieved property of certainty equation, make
It possesses larger researching value and its tempting application prospect in engineering technology.Cell neural network (Cellular
Neural Networks, CNN) it is a kind of parallel computation simulation model similar to human nerve's network, local connectivity matter is simple
Singly it is easy to ultra-large circuit (VLSI) realization, nonlinear kinetics chaos phenomenon even hyperchaos complex behavior can be produced.Carefully
Born of the same parents' neutral net prediction science, image procossing, pattern-recognition, secret communication, logic array computer structure etc.
Achieve extensive development.And Control of Chaotic Synchronization as the key link of chaos applications have become current research hotspot it
One, it is to dynamic stability no less important, therefore the Synchronization Control research to dynamic stability has reality
Meaning and practical value.
Since nineteen ninety L.M.Pecora and T.L.Carrol propose the thought of Chaotic Synchronous, the research of Chaotic Synchronous
Flourished.The synchronous method occurred at present has：Driving-response method, active-passive means, control observation device method, master
Dynamic control methods, one way coupled map, adaptive synchronization method etc..Most synchronization scenario is all based on to system structure and parameter all
It is accurate understand on the basis of realize but indeed, it is difficult to accurately obtain systematic parameter by externally measured, and even if having
A little systems have known its structure and parameter, due to the interference of external disturbance and noise, it is also difficult to so that the ginseng of two chaos systems
Count up to exactly the same.
Fractional calculus and integer rank calculus almost have equally long developing history, and integer rank calculus is fraction
The special case of rank calculus, integer level system are the idealization processing to actual chaos system.For in practical engineering application, fraction
The characteristics of level is united and structure are closer to reality, with the continuous development of fractional calculus, the synchronization of chaotic systems with fractional order
The Synchronization Control of control ratio integer rank chaos system has more prominent application value and hair in fields such as secret communication, system controls
Exhibition prospect.Up to now numerous research, which is compared, to be concentrated in the Synchronization Control of integer rank chaos system, is realized using fractional order
Cell neural network Self-adaptive synchronization control and parameter identification are but rarely reported.
Up to now, although numerous scholars are for the dynamic characteristic of cell neural network, dynamic behavior and various engineerings
Using etc. there is more thesis and work to deliver, such as Equilibrium point of the cell neural network based on threshold stimulus function, base
Identified in the airbound target of cell neural network, the application of memristor cell neural network in License Plate etc., but these grind
Study carefully the cell neural network for being substantially based on integer rank.Since the theoretical proposition of fractional order, chaotic systems with fractional order has
Larger development, such as the fully synchronized and reverse sync of fractional order Chen chaos systems, fractional order Liu chaos systems and its electricity
The research of road experiment and control, fractional order Lorenz hyperchaotic systems and its circuit simulation etc., but the god of the cell based on fractional order
It is seldom through the research of network chaos system, realize cell neural network Self-adaptive synchronization control and parameter identification more using fractional order
It is to be rarely reported.But fractional calculus can more accurately describe the various dynamics of real world and the reality of system
Physical phenomenon.Therefore the Synchronization Control research for fractional order has important theoretical research value and application prospect.
The content of the invention
The present invention have devised one newly on the basis of the respective advantage of comprehensive cell neural network and fractional order circuit
Fractional order cell neural network circuit system.And responded using known to one drive system nonlinear parameter of the system constructing
The unknown drive response system of mission nonlinear parameter value, by Adaptive synchronization controller and regulation come realize the driving-
Response system is synchronous.Since its fractional order characteristic is closer to real physical significance, it is with important actual exploitation value
Value.
What the present invention was achieved through the following technical solutions.
Step (1)：According to cytocidal action lattice basic model, integer rank three-dimensional cell nerve network system is designed, and lead to
Crossing adjusting parameter causes system to have chaotic characteristic.
Step (2)：Select fractional order differential definition and algorithm.
Step (3)：Build fractional order synchronous control system model.
Step (4)：Based on the integer rank three-dimensional cell neutral net of step (1) structure, in combination with step (2) fractional order
Calculus is theoretical, designs corresponding fractional order dynamic stability.Fractional order cell god in construction step (3) respectively
Drive system and response system through network.
Step (5)：Isochronous controller and parameter adaptive regulation are designed, driving and response system are realized in numerical simulation
The synchronization of system.
Step (6)：Fractional order cell neural network drive system and response system circuit theory in design procedure (4)
Figure, while circuit simulation is realized to the controller and adaptive regulation of step (5).
Further, a kind of fractional order cell neural network Self-adaptive synchronization control method of the present invention, it has
Body step is as follows：
(S1)：According to cytocidal action lattice basic model, integer rank three-dimensional cell nerve network system is first designed, adjusts shape
Parameters a in state equationj,ajk,Sjk,(j=1,2,3, k=1,2,3), makes system output chaos phenomenon；
And application MATLAB softwares carry out numerical simulation to the system of design, and observe its chaotic characteristic and attractor phase
Figure；
(S2)：Definition and algorithm for fractional order differential have Cauchy integral formulas, Grunwald-Letnikov fractions
Rank Definitions On Integration, the definition of Riemann-Liouville fractional order differentials, Caputo definition etc., present invention selection uses Caputo
The fractional calculus of definition, its mathematic(al) representation are as follows：
Γ () in formula is Gamma functions, and n-1≤q≤n, q are fraction, and n is integer；
The corresponding Fractional Differential Equation of dynamic system can be expressed as：
Wherein vn,vn-1…v0And αm,αm-1…α0Corresponding fractional order rank value, a are represented respectivelyn,…,a0And bm,…,b0For
Real number；F (x, y) inputs for system in formula, and G (x, y) exports for system；
(S3)：Build fractional order synchronous control system model：
Wherein X ∈ RnBe drive system a n dimension state vector, h:Rn→Rn, h is split as linear processes two
Part, then drive system I be：
In formula：X ∈ R are the state variables of drive system, g:Rn→RnFor the continuous vector function comprising linear term, G (x)
ATFor non-linear partial, G:Rn→Rn×nFor parameter vector function, A is the parameter matrix of the nonlinear function of drive system；
Response system II is accordingly：
Y ∈ R in formula are in response to the state variable of system, U ∈ RnDevice in order to control,It is the nonlinear function of drive system
Parameter matrix；
(S4)：Based on the integer rank three-dimensional cell neutral net of step (S1) structure, in combination with step (S2) fractional order
Calculus Theoretical Design goes out corresponding fractional order dynamic stability, determines with reference to formula (5) drive system I in step (S3)
Justice, constructs the drive system equation of the three-dimensional fractional order cell neural network：
Nonlinear parameter a in formula11,a12,a22It is given value, determines with reference to formula (6) response system II in step (S3)
Justice, constructs the response system equation of three-dimensional fractional order cell neural network：
Nonlinear parameter in formulaIt is unknown-value.
(S5)：The isochronous controller U and parameter adaptive regulation of (6) formula, utilize mathematical theory in design procedure (S3)
Emulation and synchronous verification are carried out into line justification synchronism matter, and with MATLAB programs；
Driving and the error responded are：
Isochronous controller U：
U=[u1,u2,u3] (10)
Wherein：
Selecting system adaptively adjusts rule and is at the same time：
Wherein ei(i=1,2,3) it is drive system and the error of response system；
(S6)：Fractional order dynamic stability drive system (7) and response system (8) circuit diagram is designed, and
Circuit simulation is realized with Multisim design controllers (10) and adaptive regulation (12).
The circuit design method of fractional order cell neural network Self-adaptive synchronization control method of the present invention, its feature
It is to comprise the following steps：
(SS1) designed according to the integer rank three-dimensional cell nerve network system formula (1) built in claim 1 step (S1)
Go out its corresponding integer rank circuit；
(SS2) design is being wanted involved in step (SS1) integer rank three-dimensional cell nerve network system circuit design to right
Seek the nonlinear object function in 1 step (S1) cell neural networkModule；
(SS3) the definite fractional order value (q1=q2=q3=0.95) of selection, and design the fractional order value and correspond to rank value
Fractional order element circuit, including chain, tree-shaped, mixed type or new；
(SS4) capacitance in suitable fractional order element circuit replacement step (SS1) in designed integer rank circuit is selected,
Obtain the corresponding fractional order driving system circuit of system；
(SS5) formula (10) formula controller U and the adaptive regulation of formula (12) formula are updated in claim 1 step (S4)
Response system formula (8), the system of meeting with a response is：
Design nonlinear factorWithIntegrating circuit, design response further in accordance with response system equation (13)
Circuit system；
(SS6) circuit integrated emulation, verification are carried out to response circuit in drive circuit in step (SS4) and step (SS5)
The synchronous property of design system.
The method have the characteristics that：The system is fractional order cell neural network system compared with traditional cell neural network
Unite, the nonlinear parameter of drive system is it is known that and the nonlinear parameter of response system in designed drive response synchronization system
It is unknown.But the drive response system is still set to realize Synchronization Control by designing isochronous controller and parameter adaptive regulation.Knot
Fractional order circuit theory and multiplexed combination circuit thought are closed, have devised corresponding synchronization control circuit schematic diagram.Simulation result
Show that circuit simulation has similar synchronous phasor with numerical simulation, demonstrate the correctness of Systems Theory analysis and actual thing
Realizability in reason.
Brief description of the drawings
The chaos attractor phasor that Fig. 1 fractional order dynamic stabilities numerical computations produce.(a) it is variable x1-x2,
(b) it is variable x2-x3, (c) is variable x1-x3。
Fig. 2 fractional order CNN adaptive synchronicity system model variables and error curve diagram.Wherein (a) becomes for driving and response
Measure xi-yi(i=1,2,3) variation track curve map, (b) are system model error ei(i=1,2,3) Asymptotic Synchronization figure.
Fig. 3 fractional order CNN drive systems (driver) circuit diagram.Wherein (a) fractional order CNN drive systems
(driver) circuit diagram, (b) are drive system (driver) equivalent circuit diagram.
Fig. 4 fractional order CNN driving system circuit simulation result phasors.(a) it is variable x1-x2, (b) is variable x2-x3, (c)
For variable x1-x3。
Fig. 5 fractional order CNN response system circuit diagrams.
Fig. 6 fractional order CNN drive response systems xi-yi(i=1,2,3) Simulation results.(a) it is variable x1-y1,
(b) it is variable x2-y2, (c) is variable x3-y3。
Fig. 7 f (x) module FX circuit diagrams and its simulation waveform.(a) it is circuit diagram, (b) is circuit simulation ripple
Shape, (c) are equivalent circuit diagram.
Fig. 8 fractional order each unit circuit diagrams.Wherein, (a) is chain element circuit；(b) tree-shaped element circuit；(c) it is mixed
Mold closing unit circuit；(d) it is novel unit circuit.
Embodiment
The present invention is described in further detail below with reference to attached drawing.
Embodiment：
1st, the fractional calculus defined using Caputo, its mathematic(al) representation are as follows：
Γ () in formula is Gamma functions, and n-1≤q≤n, q are fraction, and n is integer, and the Laplace of the formula is converted
Expression formula is：
If the primary condition of function f (t) is zero, formula (14) can be simplified shown as：
For a dynamic system, its corresponding Fractional Differential Equation can be expressed as：
Wherein vn,vn-1…v0And αm,αm-1…α0Corresponding fractional order rank value is represented respectively.F (x, y) is defeated for system in formula
Enter, G (x, y) exports for system, it is assumed that they are satisfied by the condition that initial value is 0.Laplace conversion is done to it, can be obtained
The transmission function of Fractional Differential Equation is：
It is not difficult to find out from formula (17)：Transfer function H (s)=1/s can be used in a frequency domainqTo represent that fractional order differential is calculated
Sub- q.
2nd, in order to which new fractional order cell neural network can produce stable chaos phenomenon, the matrix parameter of system (7) is made
Selected as：
Fractional order drive system (7) equation, which becomes, to be turned to：
(18) three Lyapunov indexes in formula are respectively L1=5.0529, L2=-1.2626, L3=-1.7904, its
Maximum is more than zero.And the Lyapunov dimensions of system are：
Therefore the system generates chaos phenomenon, while MATLAB carries out numerical simulation to the system of design and to observe it mixed
Ignorant characteristic which creates chaos phenomenon with attractor phasor as shown in Figure 1, also indicating that.
3rd, according to (6) formulaCorresponding fractional order response system is：
(19) nonlinear parameter in formulaIt is unknown-value.
3rd, isochronous controller and parameter adaptive regulation are designed.
Isochronous controller U is deployable to be：
Wherein ei=yi-xi,
Building a Lyapunov-krasovskii functional function is：
Selecting system adaptively adjusts rule and is at the same time：
Conclusion can be obtained by theory deduction：Work as s11≤ 1, s22≤ 1, s33When≤1, V'(t in formula (20))≤0, that is, have：Set up, and obviously have V (t) >=0, therefore error
Therefore response system Y tends to be synchronous with drive system X, i.e. when t → ∞ has, Y-X → 0,
It is as shown in Figure 2 with MATLAB Numerical Simulation Results.
4th, it is thin using linear resistance, linear capacitance, operational amplifier LM741 and fractional order element circuit, design fractional order
Born of the same parents' neutral net driving system circuit schematic diagram as shown in figure 3, and carry out circuit simulation, simulation result and Numerical Simulation Results figure
1 is similar, and simulation result is as shown in Figure 4.
5th, nonlinear factor is designed according to the equation of adaptive regulationWithIntegrating circuit figure, further in accordance with sound
System equation is answered to design response system circuit；Overall Self-adaptive synchronization control system can be designed with reference to drive system Fig. 3
Circuit theory Fig. 5 institutes, and be driven-respond synchronization simulation using Multisim, simulation result is as shown in Figure 6
6th, the nonlinear object function in cell neural network (1) is arrived involved in driving and response circuitModule, it designs realization with amplifier TL082CD under the conditions of ± 18V；The circuit diagram of design
As shown in Figure 7.
7th, the present invention is actual can be achieved 4096 kinds of multiplexed combination fractional order circuits, for brevity, choose fractional order qi(i
=1,2,3) identical value (i.e. q1=q2=q3=0.95) chain, tree-shaped, mixed type, new four kinds of combinations.Its complex frequency domain is expressed
Formula is respectively：
(a) chain
(b) tree-shaped
(c) mixed type
(d) it is new
The component parameters of each unit circuit are as shown in table 1, and corresponding circuit diagram is as shown in Figure 8.
1 fractional order each unit circuit element parameter of table
Claims (2)
- A kind of 1. fractional order cell neural network Self-adaptive synchronization control method, it is characterized in that comprising the following steps：(S1) according to cytocidal action lattice basic model, integer rank three-dimensional cell nerve network system, adjustment state side are first designed Parameters a in journeyj,ajk,Sjk,Make system output chaos phenomenon；And application MATLAB softwares carry out numerical simulation to the system of design；(S2) fractional order differential algorithm is selected：The fractional calculus that selection Caputo is defined, its mathematic(al) representation are as follows：Γ () in formula is Gamma functions, and n-1≤q≤n, q are fraction, and n is integer；The corresponding Fractional Differential Equation of dynamic system can be expressed as：Wherein vn,vn-1…v0And αm,αm-1…α0Corresponding fractional order rank value, a are represented respectivelyn,…,a0And bm,…,b0For real number；F (x, y) inputs for system in formula, and G (x, y) exports for system；(S3) fractional order synchronous control system model is built：Wherein X ∈ RnBe drive system a n dimension state vector, h:Rn→Rn, h is split as linear processes two parts, Then drive system I is：In formula：X ∈ R are the state variables of drive system, g:Rn→RnFor the continuous vector function comprising linear term, G (x) ATFor Non-linear partial, G:Rn→Rn×nFor parameter vector function, A is the parameter matrix of the nonlinear function of drive system；Response system II is accordingly：Y ∈ R in formula are in response to the state variable of system, U ∈ RnDevice in order to control,It is the ginseng of the nonlinear function of drive system Matrix number；(S4) the integer rank three-dimensional cell nerve network system based on step (S1) structure, it is micro- in combination with step (S2) fractional order Integral equation designs corresponding fractional order dynamic stability；With reference to formula (5) drive system I definition in (S3), structure Make the drive system equation of the three-dimensional fractional order cell neural network：Nonlinear parameter a in formula11,a12,a22It is given value；With reference to formula (6) response system II definition in (S3), construction three Tie up the response system equation of fractional order cell neural network：Nonlinear parameter in formulaIt is unknown-value；(S5) in design procedure (S3) (5) formula isochronous controller U and parameter adaptive regulation, demonstrate,proved using mathematical theory Bright synchronization property, and carry out emulation and synchronous verification with MATLAB programs；The error of drive system and response system is：Isochronous controller U：U=[u1,u2,u3] (10)Wherein：Selecting system adaptively adjusts rule and is at the same time：Wherein ei(i=1,2,3) it is drive system and the error of response system；(S6) fractional order dynamic stability drive system formula (7) and response system formula (8) circuit diagram is designed, is used in combination Multisim design controller formulas (10) and adaptive regulation formula (12) realize circuit simulation.
- A kind of 2. circuit design side of fractional order cell neural network Self-adaptive synchronization control method as claimed in claim 1 Method, it is characterized in that comprising the following steps：(SS1) it is designed according to the integer rank three-dimensional cell nerve network system formula (1) built in claim 1 step (S1) Corresponding integer rank circuit；(SS2) design arrives claim 1 step involved in step (SS1) integer rank three-dimensional cell nerve network system circuit design Suddenly the nonlinear object function in (S1) cell neural networkModule；(SS3) the definite fractional order value (q1=q2=q3=0.95) of selection, and design the fraction that the fractional order value corresponds to rank value Rank element circuit, including chain, tree-shaped, mixed type or new；(SS4) capacitance in suitable fractional order element circuit replacement step (SS1) in designed integer rank circuit is selected, is obtained The corresponding fractional order driving system circuit of system；(SS5) sound being updated to formula (10) formula controller U and formula (12) formula adaptive regulation in claim 1 step (S4) Systematic (8) is answered, the system of meeting with a response is：Design nonlinear factorWithIntegrating circuit, further in accordance with response system equation (13) design response system electricity Road；(SS6) circuit integrated emulation is carried out to response circuit in drive circuit in step (SS4) and step (SS5).
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| CN106160996A (en) * | 2016-07-04 | 2016-11-23 | 江西理工大学 | The circuit design method of any fractional order value based on general Lucas number |
| CN108762067A (en) * | 2018-04-28 | 2018-11-06 | 南京理工大学 | A kind of the networking Synchronizing Control Devices and acquisition methods of memristor neural network |
| CN109086874A (en) * | 2018-08-07 | 2018-12-25 | 穆天机器人（杭州）有限公司 | A kind of general neural network model based on Fractal structural theory |
| CN110324137B (en) * | 2019-02-27 | 2021-06-29 | 齐鲁工业大学 | Fractional order hidden chaotic system with linear balance point |
| CN110488634B (en) * | 2019-09-03 | 2022-06-10 | 江西理工大学 | Method for realizing reverse synchronization and rotation reverse synchronization in coupled oscillator system |
| CN113095497B (en) * | 2021-05-06 | 2023-04-07 | 安徽大学 | Finite time synchronization method and device for fractional order quaternary memristor neural network |
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