CN101408752B - Neural network extreme control method and system based on chaos annealing and parameter destabilization - Google Patents

Abstract

The invention provides a neutral network extreme value control method based on chaotic annealing and parameter perturbation, and a system thereof. The control method transforms a control problem of an extreme value search system to solve an extreme value point problem with zero rate of slope in an output function of a controlled system. According to the extreme value point solving problem, a pair of dual problems with constraint conditions are constructed. A neutral network solving dual problem based on chaotic annealing and parameter perturbation is established, which comprises a chaotic annealing initial search phase, a parameter perturbation middle search phase and a final search phase of a natural network. The global optimum search variable can be obtained by the solving of the neutral network extreme value control method. According to the obtained global optimum search variable, the output value of the extreme value search system is driven to converge to a global extreme value point of the output function, thus realizing the control purpose of the extreme value search system. The control system provided by the invention is divided into a module simulation mode and a real time control mode and realizes the application of the control method in the extreme value search system respectively from two aspects of off-line module simulation and real time system control.

Description

Neural network extreme control method based on chaos annealing and parameter perturbation and system

Technical field

The present invention relates to artificial intelligence control technology field, more specifically, the present invention relates to a kind of neural network extreme control method and system based on chaos annealing and parameter perturbation.

Background technology

Extremum search system (Extremum Seeking System) is the real system that a class is extensively present in the fields such as popular production and life, Industry Control and Military Application, for example the brake control system of injection engine firing chamber control system, automobile and the aircraft of gas turbine, the tight formation flight control of aircraft, tubular reactor heap control system and human body exercise machine control system, all belongs to the category of extremum search system.In a lot of actual extremum search systems, reference locus between the reference input of system and output is difficult to the person of being designed and accurately knows, and due to the uncertainty of system model and the impact of parameter time varying, finally cause the corresponding search variables of extreme point on reference locus to be difficult to be determined.How making extremum search system being subject to, under the impact of uncertain and parameter time varying, still can finding adaptively the extreme point of reference locus, make the performance of controlled system perform to optimum condition, is the problem that the scholar of boundary is controlled in a permanent puzzlement.The appearance of extreme control method solves this type of actual control problem a kind of effective means is provided with developing into.

At present, the extreme control method for extremum search system mainly concentrates on: the extreme control method based on sinusoidal excitation signal and sliding formwork extreme control method.Owing to all adopting sinusoidal periodic signal as the pumping signal of system in this two classes extreme control method, caused being mingled with all the time in the search signal of controlled system the sinusoidal periodic signal of little amplitude, thereby can not make the output valve asymptotic convergence of controlled system to required extreme point, cause the sinusoidal fluctuation phenomenon at Near The Extreme Point; And for the output function of extremum search system, there is the situation of a plurality of extreme points, above-mentioned two class extreme control methods all cannot guarantee that the output valve of controlled system converges to its global extremum point, thereby cause the optimum performance that extremum search system has not fully played, cause the waste of the energy.Existing these defects of extreme control method, have limited the method to a certain extent in actual extremum search system, and the application in function optimization problem.

Because extreme control method has huge application potential in commercial production and Military Application field, can greatly save the energy, improve to greatest extent industrial productivity and military engagement power, for overcoming the defect of existing extreme control method, study new extreme control method and have very important significance.

Summary of the invention

For overcoming the defect of existing extreme control method, the invention provides a kind of neural network extreme control method and system based on chaos annealing and parameter perturbation.

According to an aspect of the present invention, provide a kind of neural network extreme control method based on chaos annealing and parameter perturbation, having comprised:

Step 10), the control problem of extremum search system being converted into slope in the output function that solves this controlled system is zero extreme point problem;

Step 20), according to described extreme point Solve problems, construct a pair of primal-dual optimization problem with constraint condition;

Step 30), according to the described dual problem with constraint condition, set up a kind of neural network extreme control method based on chaos annealing and parameter perturbation;

Step 40), by the solving of described neural network extreme control method, corresponding optimum search variable in the time of can obtaining extremum search system and be output as global extremum;

Step 50), according to the search variables of the global optimum of gained, the output valve of ordering about extremum search system converges to the global extremum point of output function, thereby realizes the control object of extremum search system.

Wherein, step 20) further comprise: according to described extreme point Solve problems, determine the extreme-value problem that minimizes with constraint condition, application dual Control is theoretical, there is another maximization extreme-value problem with constraint condition, thereby form a pair of dual problem with constraint condition.

Wherein, step 30) neural network extreme control method based on chaos annealing and parameter perturbation in comprises that three different search control the stages, specifically comprises:

Step 310), the starting stage of this extreme control method belongs to the chaos annealing search phase, the chaotic noise that utilizes Lorenz model to produce, directly be introduced into having in the neural network of parameter perturbation, by the amplitude of continuous Decaying chaotic noise and the acceptance probability of chaotic noise, realize the search procedure of chaos annealing;

Step 320), the interstage of this extreme control method belongs to the parameter perturbation search phase, utilize parameter perturbation strategy, make the output valve of neural network temporarily break away from the attraction of the convergence point of initial search phase, thereby verify whether initial convergence point is global extremum point.By the decay gradually of the parameter perturbation factor, make search procedure progress into the terminal stage of extreme control method;

Step 330), the terminal stage of this extreme control method belongs to the neural network search phase, utilizes the convergence of neural network self to make the search variables of extremum search system accurately and progressively converge to its global extremum point.

According to a second aspect of the invention, provide a kind of neural network extreme control system based on chaos annealing and parameter perturbation, having comprised:

Model emulation pattern, for determining the various adjusting parameters of the neural network extreme control method based on chaos annealing and parameter perturbation, verify global search and the control ability of described control method in different extreme value search systems, expand the application of described control method in various function optimization problems;

Real-time control mode, by multiple different sensor mechanism, measure the quantity of state of reflection controlled device characteristic, and by corresponding data acquisition modes, the status information feedback of actual measurement is returned to the real-time control mode in computing machine, utilize described control method, calculate in real time corresponding control signal, by data driven unit, digiverter and signal amplifying apparatus, control signal offers topworks the most at last, for controlling the output valve of extremum search controlled device, make it asymptotic convergence to the global extremum point of output function.

Wherein, described model emulation pattern and real-time control mode not only have limiting control ability to the extremum search system of having preserved, and can expand and accept new extremum search system model, and it is carried out to limiting control.

Wherein, the real-time extremum search control system consisting of described real-time control mode further comprises: multichannel sensor mechanism, data acquisition module, digital signal driving mechanism, digital-to-analog conversion mechanism, voltage and power amplifier and topworks.

Wherein, in described real-time extremum search control system, multichannel sensor mechanism is connected with extremum search control object, for measuring the quantity of state of reflection controlled device characteristic, comprising: the status signals such as temperature, pressure, distance, rotating speed, angle; Data acquisition module, is positioned between multichannel sensor mechanism and described real-time control mode (controller), for gathering different measuring-signals, and the measuring-signal collecting is completed after analog to digital conversion, offers real-time control mode; Digital signal driving mechanism is connected with described real-time control mode, for improving the long-distance transmissions ability of digital signal; Digital-to-analog conversion mechanism is connected with digital signal driving mechanism, for digital signal is converted to simulating signal; Voltage, power amplifier are connected with digital-to-analog conversion mechanism, for the simulating signal after conversion is carried out to suitable voltage and power amplification; Topworks is connected with voltage, power amplifier, for accepting control signal, carries out operation accordingly, completes the output limiting control to extremum search control object.

The output signal of the extremum search controlled system of the neural network extreme control method utilization feedback based on chaos annealing and parameter perturbation that the present invention proposes, calculate corresponding search signal and control signal, the output valve of ordering about controlled system accurately and progressively converges to required global extremum point; For different function optimization problems, also can apply described control method; Described control method can be saved the energy to greatest extent, gives full play to the performance of controlled system, contributes to develop the production model of economizing type.

Accompanying drawing explanation

Fig. 1 is neural network extreme control method based on chaos annealing and parameter perturbation and the main surface chart of Matlab software of system;

Fig. 2 is the main surface chart of the model emulation pattern in the neural network extreme control system based on chaos annealing and parameter perturbation;

Fig. 3 is the main surface chart of the real-time control mode in the neural network extreme control system based on chaos annealing and parameter perturbation;

Fig. 4 is the composition frame diagram of real-time extremum search control system;

Fig. 5 is the output valve of Schaffer function and the value distribution plan between independent variable;

The output valve simulation comparison figure of the Schaffer function of Fig. 6 when adopting respectively neural network extreme control method based on chaos annealing and parameter perturbation with extreme control method based on sliding moding structure;

The state variable x of the second order Schaffer function of Fig. 7 when adopting respectively neural network extreme control method based on chaos annealing and parameter perturbation with extreme control method based on sliding moding structure ₁simulation comparison figure;

The state variable x of the second order Schaffer function of Fig. 8 when adopting respectively neural network extreme control method based on chaos annealing and parameter perturbation with extreme control method based on sliding moding structure ₂simulation comparison figure;

Fig. 9 is the simulation result of the model emulation pattern in the neural network extreme control system of employing based on chaos annealing and parameter perturbation in third-order system Branin output function model;

Figure 10 is the simulation result of three state variables in third-order system Branin output function model;

Figure 11 is the simulation result of the model emulation pattern in the neural network extreme control system of employing based on chaos annealing and parameter perturbation in fourth-order system Six-Hump output function model;

Figure 12 is the simulation result of one of four states variable in fourth-order system Six-Hump output function model;

Figure 13 is for adopting respectively neural network extreme control method and the poor simulation comparison figure of adjacent airfoil height in the tight formation flight of unmanned plane of the extreme control method based on sinusoidal excitation signal based on chaos annealing and parameter perturbation;

Figure 14 is for adopting respectively neural network extreme control method and the poor simulation comparison figure of adjacent wing lateral separation in the tight formation flight of unmanned plane of the extreme control method based on sinusoidal excitation signal based on chaos annealing and parameter perturbation;

Figure 15 washes power simulation comparison figure and the local comparison diagram that amplifies on adopting respectively neural network extreme control method based on chaos annealing and parameter perturbation and the extreme control method based on sinusoidal excitation signal wing plane obtains in the tight formation flight of unmanned plane;

Figure 16 is the simulation result of the average fuel air ratio value of aeromotor φ while adopting self-adaptation control method;

Figure 17 is the indoor vibration pressure P of aeroengine combustor buring while adopting self-adaptation control method _csimulation result;

The simulation result of the average fuel air ratio value of aeromotor φ when Figure 18 is the neural network extreme control method adopting based on chaos annealing and parameter perturbation;

The indoor vibration pressure P of aeroengine combustor buring when Figure 19 is the neural network extreme control method adopting based on chaos annealing and parameter perturbation _csimulation result.

Embodiment

Below in conjunction with the drawings and specific embodiments, a kind of neural network extreme control method and system based on chaos annealing and parameter perturbation provided by the invention is described in detail.

A kind of neural network extreme control method based on chaos annealing and parameter perturbation that the present invention proposes, be used for controlling extremum search system, make its output valve accurately and progressively converge to the global extremum point of output function, improved search capability and the stablizing effect of original extreme control method.From realizing, neural network extreme control method based on chaos annealing and parameter perturbation can be divided into extremum search Mechanism Design, the design of the neural network extreme control method based on parameter perturbation and chaos annealing and design three parts, and wherein the design of the neural network extreme control method based on parameter perturbation and chaos annealing design are the keys of the inventive method.The specific implementation of described method can be deposited in a control module in system.Described control module is accepted the measured signal of extremum search controlled system according to feedback, utilize described control method, and real-time resolving goes out corresponding limiting control signal, for controlling the output valve asymptotic convergence of extremum search system to the global extremum point of output function.The general extremum search system of following basis describes method proposed by the invention in detail.

One, extremum search Mechanism Design

State equation and the output function of considering a class extremum search system are:

$\stackrel{\·}{x}=f(x\left(t\right),u\left(t\right))---\left(1\right)$

y＝F(x(t))

Wherein,

with

the state vector that represents respectively system, control vector and output valve.F (x (t), u (t)) is the state equation of system, and F (x (t)) is the output function of system.In using based on sinusoidal excitation signal and the extreme control method based on sliding moding structure, F (x (t)) requirement can only have an extreme point, because have a plurality of extreme points once F (x (t)), these methods just can not guarantee that the output valve of extremum search system converges to the global extremum point of output function F (x (t)).And the output function F of the extremum search system of the method for the invention research (x (t)) can have a plurality of extreme points.

Because extremum search system (1) is controllable system, (x (t), θ) can stablize this system, wherein so necessarily control law u (t)=β

it is the locating vector of this system.By control law u (t)=β (x (t), the state equation of θ) substitution system, known when system stability, necessarily there is following relation:

$f(x,\mathrm{\β}(x,\mathrm{\θ}))=0\↔x=l\left(\mathrm{\θ}\right)---\left(2\right)$

Wherein, l:R ^m→ R ⁿit is smooth function.(2) formula is updated to the output function of extremum search system, can obtains new output function relation:

(3)

In extremum search system, at least there is one group of extremal vector

make the output valve y of system converge to the extreme point y of output function ^*, thereby, according to the differential theory of mathematics, there is following relation:

And,

or

After being differentiated to the time in output function (3) two ends, can obtain following formula:

$\∂\left(\mathrm{\θ}\left(t\right)\right)\·\stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{y}\left(t\right)---\left(4\right)$

Wherein,

In the control of extremum search system, require the output valve y of controlled device to converge on its extreme point y ^*, that is to say so and require locating vector θ must converge on its extremal vector θ ^*thereby, just can make system output meet

once locating vector θ converges on its extremal vector θ ^*during place, output function is for the absolute value of the partial derivative of vectorial each component of θ so

to equal zero.The object of the neural network extreme control method based on chaos annealing and parameter perturbation that the present invention proposes makes exactly

each component in the shortest time, all converge to minimum value separately, this optimizing process must be subject to the constraint of (4) formula certainly.

Therefore, extremum search control problem can be converted into:

Consider condition: ${\∂}^T\left(\mathrm{\θ}\right)-\mathrm{sign}(\∂\left(\mathrm{\θ}\right))|\∂\left(\mathrm{\θ}\right)|=0,$ Can by (5) formula abstract be (6) formula, then can solve extremum search problem by the neural network of structure based on chaos annealing and parameter perturbation.

Wherein, $\mathrm{\&upsi;}={\left[\begin{array}{c}{\&PartialD;}^T\left(\mathrm{\&theta;}\right)\\ \left|{\&PartialD;}^T\left(\mathrm{\&theta;}\right)\right|\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)\end{array}\right]}_{3m\&times;1},$ c＝[0 _1×m1 _1×m0 _1×m] ^T， $M=\left[\begin{array}{ccc}{1}_{1\&times;m}& -\mathrm{sign}(\&PartialD;\left(\mathrm{\&theta;}\right))& 0_{1\&times;m}\\ {\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^T\left(t\right)& 0_{1\&times;\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="H2008101694813E00041.png,H2008101694813E00042.png"\; state="\{\{state\}\}">m</figure-callout>}}& 0_{1\&times;\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="H2008101694813E00041.png,H2008101694813E00042.png"\; state="\{\{state\}\}">m</figure-callout>}}\\ 0_{1\&times;\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="H2008101694813E00041.png,H2008101694813E00042.png"\; state="\{\{state\}\}">m</figure-callout>}}& 0_{1\&times;m}& \&PartialD;\left(\mathrm{\&theta;}\right)\end{array}\right],$ $b=\left[\begin{array}{c}0\\ \stackrel{\&CenterDot;}{y}\left(t\right)\\ \stackrel{\&CenterDot;}{y}\left(t\right)\end{array}\right],$ $\mathrm{sign}\left(\mathrm{\&zeta;}\right)=\left\{\begin{array}{cc}1& \mathrm{\&zeta;}>0\\ 0& \mathrm{\&zeta;}=0\\ -1& \mathrm{\&zeta;}<0\end{array}\right..$

According to duality principle (person of an ordinary skill in the technical field should be understood that the duality principle in linear control theory), there is following dual form in above-mentioned extremum search problem:

Wherein, $\mathrm{\&omega;}={\left[\begin{array}{ccc}{\mathrm{\&omega;}}_1& {\mathrm{\&omega;}}_2& {\mathrm{\&omega;}}_3\end{array}\right]}_{3\&times;1}^T$ Dual variable for υ.

By above-mentioned analysis, the limiting control problem of an extremum search system can be converted into: under the constraint condition meeting as shown in (6) formula and (7) formula, apply the designed neural network based on chaos annealing and parameter perturbation and make g ₁(υ) and g ₂(ω) optimized problem.The design of this extremum search mechanism, can be in the situation that do not adopt the search mechanisms of sinusoidal excitation signal or sliding moding structure link, the neural network extreme control method of application based on chaos annealing and parameter perturbation guarantees that the output valve of extremum search system accurately and smoothly converges to the global extremum point of output function, eliminate the wave phenomenon of system state variables and output quantity, improve the global extremum search capability of extremum search algorithm simultaneously.

Two, there is the neural network extreme control method design of parameter perturbation

The neural network extreme control method with parameter perturbation of the present invention design is that parameter perturbation item D (t) is introduced directly among the energy function of neural network, by the design to neural network extreme control method, the impact of parameter perturbation item D (t) will be directly connected to stability and the optimality of neural network output valve.

The energy function that design has the neural network of parameter perturbation is:

$E(\mathrm{\&upsi;},\mathrm{\&omega;})=\frac{1}{2}D\left(t\right){(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))}^2+\frac{1}{2}{\left|\right|p_1\left(\mathrm{\&upsi;}\right)\left|\right|}^2+\frac{1}{2}{\left|\right|p_2\left(\mathrm{\&omega;}\right)\left|\right|}^2---\left(8\right)$

Wherein, the Euclid norm of ‖ ‖ representative function, the mathematical form D of excitation parameter (t) adopts D (t)=γ α ^{-η t}or D (t)=γ (1+t) ^-η, and α >1, γ >0 and η >0 are design variables.By regulating, α, γ and η's can change the impact of disturbed factor D (t) on neural network.

The dynamic equation with the neural network extreme control method of parameter perturbation is defined as along the negative direction of energy function (8) formula gradient and successively decreases, and concrete form is:

$\frac{\mathrm{d\&sigma;}}{\mathrm{dt}}=-\mathrm{\&mu;}\&dtri;E\left(\mathrm{\&sigma;}\right)---\left(9\right)$

Wherein, vectorial σ=(υ, ω) ^t,

the gradient that represents energy function E (σ), μ is scale-up factor, and is positive number, by regulating μ can change the speed of convergence with parameter perturbation neural network.Make u ₁, u ₂represent respectively neuronic internal state variable, its concrete form is:

$\frac{{\mathrm{<figure-callout\; id="1"\; label="du"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">du</figure-callout>}}_1}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{\&PartialD;E(\mathrm{\&upsi;},\mathrm{\&omega;})}{\&PartialD;\mathrm{\&upsi;}}=-\mathrm{\&mu;}[D\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]$

$=-\mathrm{\&mu;}[D\left(t\right)c(c^T\mathrm{\&upsi;}-b^T\mathrm{\&omega;})+M^T(\mathrm{M\&upsi;}-b)]---\left(10\right)$

$\frac{{\mathrm{<figure-callout\; id="2"\; label="du"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">du</figure-callout>}}_2}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{\&PartialD;E(\mathrm{\&upsi;},\mathrm{\&omega;})}{\&PartialD;\mathrm{\&omega;}}=-\mathrm{\&mu;}[-D\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]$

$=-\mathrm{\&mu;}[-D\left(t\right)b(c^T\mathrm{\&upsi;}-b^T\mathrm{\&omega;})+M(M^T\mathrm{\&omega;}-c)]---\left(11\right)$

υ＝q(u ₁) (12)

ω＝q(u ₂) (13)

Wherein, υ and ω are the output vectors of this neural network, u ₁and u ₂be respectively to have the vector with dimension with υ and ω, q () represents to have the activation function of S type, and the concrete form of S type activation function is: $\mathrm{\&upsi;}=q\left(u_1\right)=\frac{1}{1+\exp (-{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1/{\mathrm{\&epsiv;}}_1)}-0.5$ With $\mathrm{\&omega;}=q\left(u_2\right)=\frac{1}{1+\exp (-{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2/{\mathrm{\&epsiv;}}_2)}-0.5,$ And parameter ε ₁>0, ε ₂>0.Power connection matrix between the unit of this neural network is $\left[\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right]=\left[\begin{array}{cc}-\mathrm{\&mu;}(D\left(t\right){\mathrm{cc}}^T+M^{T}M)& \mathrm{\&mu;D}\left(t\right){\mathrm{cb}}^T\\ \mathrm{\&mu;D}\left(t\right){\mathrm{bc}}^T& -\mathrm{\&mu;}(D\left(t\right){\mathrm{bb}}^T+{\mathrm{MM}}^T)\end{array}\right],$ Threshold vector is

by changing scale-up factor μ, can regulate the size of power connection matrix and threshold vector.

Three, the design of the neural network extreme control method based on chaos annealing and parameter perturbation

In order to make control method of the present invention all there is good global extremum search capability for the extremum search system with arbitrary form output function, on the basis of the above-mentioned neural network extreme control method with parameter perturbation, introduced chaos annealing link.Application Lorenz model produces chaotic noise, and is introduced in the above-mentioned neural network with parameter perturbation, as the chaos annealing link of neural network.Utilize randomness and the ergodicity of chaos, improve the ability of searching optimum of neural network.By theoretical analysis, prove: the neural network extreme control method based on chaos annealing and parameter perturbation can be with probability 1 asymptotic convergence the globally optimal solution to the extreme-value problem of (6) formula and (7) formula.

The concrete form of the neural network extreme control method based on chaos annealing and parameter perturbation is:

$\frac{{\mathrm{<figure-callout\; id="1"\; label="du"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">du</figure-callout>}}_1}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[D_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]+{\mathrm{\&Gamma;}}_1({\mathrm{\&chi;}}_1({\mathrm{\&tau;}}_1-{\mathrm{\&rho;}}_1)+{\mathrm{\&rho;}}_1)& \mathrm{randnum}<P_1\left(t\right)\\ -\mathrm{\&mu;}[D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]& \mathrm{otherwise}\end{array}\right.$

(14)

$\frac{{\mathrm{<figure-callout\; id="2"\; label="du"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">du</figure-callout>}}_2}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[{-D}_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]+{\mathrm{\&Gamma;}}_2({\mathrm{\&chi;}}_2({\mathrm{\&tau;}}_2-{\mathrm{\&rho;}}_2)+{\mathrm{\&rho;}}_2)& \mathrm{randnum}<P_2\left(t\right)\\ -\mathrm{\&mu;}[-D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]& \mathrm{otherwise}\end{array}\right.$

(15)

D ₁(t)＝C (16)

D ₂(t)＝γα ^-ηt (17)

$\mathrm{\&upsi;}=q\left(u_1\right)=\frac{1}{1+\exp (-{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1/{\mathrm{\&epsiv;}}_1)}-0.5---\left(18\right)$

$\mathrm{\&omega;}=q\left(u_2\right)=\frac{1}{1+\exp (-{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2/{\mathrm{\&epsiv;}}_2)}-0.5---\left(19\right)$

$\frac{{\mathrm{d\&Gamma;}}_i\left(t\right)}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&kappa;}& {\mathrm{\&Gamma;}}_i\left(t\right)>0\\ 0& \mathrm{otherwise}\end{array}\right.,i=\mathrm{1,2}---\left(20\right)$

$P_1\left(t\right)=\exp [-\left(\frac{\mathrm{\&upsi;}\&prime;}{K_{B}T}\right)]---\left(21\right)$

$P_2\left(t\right)=\exp [-\left(\frac{\mathrm{\&omega;}\&prime;}{K_{B}T}\right)]---\left(22\right)$

$\left\{\begin{array}{c}\frac{d{\mathrm{\&chi;}}_1}{\mathrm{dt}}=a_a({\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1)\\ \frac{{\mathrm{d\&chi;}}_2}{\mathrm{dt}}=b_b{\mathrm{\&chi;}}_1-{\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_3\\ \frac{d{\mathrm{\&chi;}}_3}{\mathrm{dt}}={\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_2-c_c{\mathrm{\&chi;}}_3\end{array}\right.---\left(23\right)$

$T=\frac{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="H2008101694813E00041.png,H2008101694813E00042.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\ln (h+t)}---\left(24\right)$

Wherein, P _i(t), (i=1,2) represent the acceptance probability of chaotic noise, and P all the time _i(t)>=0, $\mathrm{\&upsi;}\&prime;=\frac{\mathrm{d\&upsi;}}{\mathrm{dt}},$ $\mathrm{\&omega;}\&prime;=\frac{\mathrm{d\&omega;}}{\mathrm{dt}},$ K _bbe Boltzmann constant, T is annealing temperature, T ₀initial annealing temperature, parameter h>1.Parameter randnum is illustrated in [r _a, 1] between random number, r _a∈ [0,1] is lowest confidence.Γ _i(t) be the influence coefficient of chaotic noise, and Γ all the time _i(t)>=0, κ (0< κ <1) represents the influence coefficient Γ of chaotic noise _i(t) decay factor.ε ₁>0 and ε ₂>0 is the gain coefficient of output vector υ and ω.Lorenz Model Mapping, as shown in (23) formula, is worked as a _a=10, b _b=28 Hes $c_c=\frac{8}{3}$ Time, χ _i(t) (i=1,2,3) will present chaos state.[τ ₁, ρ ₁] and [τ ₂, ρ ₂] expression chaos state χ ₁and χ (t) ₂(t) scope of space, the difference of the selective basis extremum search problem of its range size and difference, state variable u while generally selecting its size to meet neural network not introduce chaos annealing ₁and u ₂10% of maximum rate of change, and symmetrical about zero point, so Lorenz model is used as the mechanism that in the neural network extreme control method based on chaos annealing and parameter perturbation, chaos annealing produces.

Excitation parameter item D ₁and D (t) ₂(t) choose as shown in (16) and (17) formula, wherein C represents normal number.Although excitation parameter item D ₁(t) be a certain normal number, this can't affect the convergence of designed neural network.Compare with the above-mentioned designed neural network with parameter perturbation (as (10)～(13) formula), this neural network based on chaos annealing and parameter perturbation has just been introduced chaotic noise item Γ _iand χ (t) _i(t), (i=1,2), their introducing has strengthened the ability of searching optimum of neural network.P _i(t) be the acceptance probability of chaos annealing, along with increasing progressively of time, acceptance probability P _i(t) present and successively decrease.

In the operation starting stage of the neural network extreme control method based on chaos annealing and parameter perturbation, utilize the affect the nerves search capability of network output valve of chaotic noise that Lorenz model produces, make neural network output there is ergodicity, along with increasing progressively of time, acceptance probability P _i(t) be bound to be less than lowest confidence r _a, now by the defined neural network based on chaos annealing and parameter perturbation of (14)～(24) the formula defined neural network form with parameter perturbation of (10)～(13) formula of serving as reasons of just evolving gradually; Utilize disturbed factor D ₂(t) impact, makes the output valve of neural network temporarily break away from the attraction of the convergence point of initial search phase, can verify whether initial convergence point is global extremum point; Along with increasing progressively of time, disturbed factor D ₂(t) also will converge to zero, its effect will reduce gradually until can ignore, the neural network now with parameter perturbation is just evolved as general recurrent neural network gradually, utilizes the convergence of neural network self to make the output valve of extremum search system accurately and progressively converge to its global extremum point.

More than introduced the design process of control method of the present invention, the control effect of method proposed by the invention and the neural network extreme control system based on chaos annealing and parameter perturbation have been described in detail in detail below according to a particular embodiment of the invention.

The main interface of Matlab software of the neural network extreme control system based on chaos annealing and parameter perturbation as shown in Figure 1, comprises two kinds of patterns: model emulation pattern and real-time control mode.Wherein, the main interface of model emulation pattern as shown in Figure 2, the main interface of real-time control mode as shown in Figure 3, the composition frame diagram of extremum search control system as shown in Figure 4 in real time, composition and annexation that this figure has comprised each functional module in real-time extremum search control system, and the flow direction of signal in system.

Model emulation pattern in neural network extreme control system based on chaos annealing and parameter perturbation comprises: second-order system Schaffer output function model, third-order system Branin output function model, fourth-order system Six-Hump output function model, the tight formation flight control of unmanned plane, aeroengine combustor buring ACTIVE CONTROL, aircraft equilibrium state are resolved, Nash Equilibrium Solution problem, these seven simulation examples.For the simulation example that wherein there is no typing, can adopt " realistic model input field " in the model emulation pattern of native system to carry out typing again, thereby can utilize control method of the present invention to complete simulating, verifying.Utilize " parameter adjusting " pop-up box in interface can the parameters in control method of the present invention be regulated.Real-time control mode in neural network extreme control system based on chaos annealing and parameter perturbation, mainly according to the model of actual extremum search controlled device, carry out real-time process control, mode input and parameter adjustment process complete by " extremum search system model input field " and " parameter adjusting " respectively.Following examples are by the model emulation pattern of mainly applying in system of the present invention.

1, embodiment 1

For a second order extremum search system with Schaffer output function, its concrete form is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\\ {\stackrel{\&CenterDot;}{x}}_2\end{array}\right)=\left(\begin{array}{cc}1& 1\\ 0.5& 0\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)+\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)\left(\begin{array}{c}{u}_1\\ u_2\end{array}\right)---\left(25\right)$

$y=f(x_1,x_2)=\frac{{\sin }^2\sqrt{x_1^2+x_2^2}-0.5}{{[1+0.001(x_1^2+x_2^2)]}^2}-0.5---\left(26\right)$

System adopts control law to be:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=x_1-{\mathrm{\&theta;}}_1-x_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=x_2-2{\mathrm{\&theta;}}_2\end{array}\right.---\left(27\right)$

Known this Schaffer output function has a global minimum min (y (x ₁, x ₂))=y (0,0)=-1, exist infinite a plurality of local minimum to be surrounded putting apart from this global extremum in about 3.14 scopes, and there is strong vibration in this output function, when the state variable of system meets :-10≤x ₁, x ₂≤ 10 o'clock, output function y=f (x ₁, x ₂) value distribution plan as shown in Figure 5.General control searching method is difficult to obtain its Global Extreme Value.Adopt respectively control method and the extreme control method based on sliding moding structure that the present invention proposes to control above-mentioned second order extremum search system, the simulation comparison result of state variable and output valve is as shown in Fig. 6,7 and 8.Known by simulation result, the control method that adopts the present invention to propose makes the state variable of extremum search system and output valve can both converge on quickly its global extremum point, and output valve does not exist wave phenomenon after converging on global extremum point; And extreme control method based on sliding moding structure can not stable extremal search system state variable and output valve, and output valve can not converge on its global extremum point.

2, embodiment 2

Adopt the model emulation Pattern completion of system of the present invention to having the limiting control task of three rank extremum search systems of Branin output function, the model description of this extremum search system is:

${\stackrel{\&CenterDot;}{x}}_1=x_1+x_2+0.3x_3+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1$

${\stackrel{\&CenterDot;}{x}}_2=0.5x_1+2x_2+1.5x_3+u_2---\left(28\right)$

${\stackrel{\&CenterDot;}{x}}_3=1.5\sin \left(x_1\right)+{2x}_2-0.5{\mathrm{<figure-callout\; id="3"\; label="x"\; filenames="H2008101694813E00042.png"\; state="\{\{state\}\}">x</figure-callout>}}_3+{0.5\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+2{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$

$y={(x_2-\frac{5.1}{4{\mathrm{\&pi;}}^2}{x}_1^2+\frac{5}{\mathrm{\&pi;}}{x}_1-6)}^2+10(1-\frac{1}{8\mathrm{\&pi;}})\cos x_1+10---\left(29\right)$

System adopts control law to be:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=x_1-{3\mathrm{\&theta;}}_1+{2x}_3\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=2x_2-{\mathrm{\&theta;}}_2+1.5x_3\end{array}\right.---\left(30\right)$

There are three global minimums in known this output function, the output valve of final output function is all identical, i.e. miny=0.3978.The simulation software that adopts the present invention to propose can obtain the simulation result of this extremum search system, as shown in Fig. 9,10.Known by simulation result, this third-order system can be according to the location finding of initial point to apart from self nearest global extremum point, and the output valve of system does not exist sinusoidal fluctuation phenomenon after converging on this global extremum point.

3, embodiment 3

Adopt the model emulation Pattern completion of system of the present invention to a limiting control task with the Fourth Order Nonlinear extremum search system of Six-Hump Camel-Back output function, the model description of this extremum search system is:

${\stackrel{\&CenterDot;}{x}}_1=x_1+5x_2+0.3x_3-x_4+0.5{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1$

${\stackrel{\&CenterDot;}{x}}_2=0.5x_1+2x_2+1.5\sin \left(x_3\right)-{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+2{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$

(31)

${\stackrel{\&CenterDot;}{x}}_3=\sin \left(x_1\right)+2x_2-0.25\cos \left(x_3\right)+19x_4+0.5u_1-2.5{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$

${\stackrel{\&CenterDot;}{x}}_4=0.5x_1{x}_4+1.5\cos \left(x_2\right)-0.5\sin \left(x_3\right)-9x_4+1.5{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$

$y={4x}_1^2-2.1{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">x</figure-callout>}}_1^4+\frac{x_1^6}{3}+x_1{x}_2-{4\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">x</figure-callout>}}_2^2+{4x}_2^4---\left(32\right)$

System adopts control law to be:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=x_1-2{\mathrm{\&theta;}}_1+{2x}_3+x_4\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=0.25x_1+2x_2-{\mathrm{\&theta;}}_2+1.5x_3\end{array}\right.---\left(33\right)$

Known above-mentioned quadravalence extremum search system has stronger non-linear, there are Liu Ge local minizing point and two global minimums in this output function simultaneously, and the minimum value of output function is miny=-1.0316, this function is often as the trial function of evaluating optimization method quality.Based on control method of the present invention, obtain the simulation result of this Fourth Order Nonlinear extremum search system as shown in Figure 11,12.Known by simulation result, the quantity of state of this extremum search system still can promptly search the global extremum point nearest apart from initial position, and the output valve of controlled system does not exist sinusoidal fluctuation problem after stable.

4, embodiment 4

For model after the simplification of one group of tight flight formation being formed by two unmanned planes, be shown below.

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\\ {\stackrel{\&CenterDot;}{x}}_2\\ {\stackrel{\&CenterDot;}{x}}_3\\ {\stackrel{\&CenterDot;}{x}}_4\end{array}\right]=\left[\begin{array}{cccc}0& 1& 0& 0\\ -20& -9& 0& 0\\ 0& 0& 0& 1\\ 0& 0& -35& -15\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]---\left(34\right)$

Its output equation is:

y(t)＝-10(x ₁(t)) ²-5(x ₃(t)+9) ²+590 (35)

Wherein, x ₁and x ₃the adjacent wing range difference in vertical direction and the range difference in the horizontal that represent respectively two unmanned planes, x ₂and x ₄represent respectively two unmanned planes velocity contrast in vertical direction and velocity contrast in the horizontal, output valve y represent that wing plane is subject in the tail flow field of lead aircraft on wash power.Obviously, the global extremum point that above-mentioned tight formation flight model has is to work as ${\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">x</figure-callout>}}_1^{*}=0$ With ${\mathrm{<figure-callout\; id="3"\; label="x"\; filenames="H2008101694813E00042.png"\; state="\{\{state\}\}">x</figure-callout>}}_3^{*}=-9$ Time, in maximum, the power of washing is y ^*=590.

This system adopts control law to be:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="H2008101694813E00031.png,H2008101694813E00091.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=20({\mathrm{\&theta;}}_1-x_1)-9x_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=35({\mathrm{\&theta;}}_2-x_3)-15x_4\end{array}\right.---\left(36\right)$

Adopt respectively control method and the extreme control method based on sinusoidal excitation signal that the present invention proposes to control the tight formation flight system of above-mentioned unmanned plane, the simulation comparison result of state variable and output valve is as shown in Figure 13,14 and 15.Known by simulation comparison result, the control method that adopts the present invention to propose makes the state variable of extremum search system and output valve can both converge on quickly its extreme point separately, and output valve y converges on and in maximum, washes power y ^*after there is not wave phenomenon; And extreme control method based on sinusoidal excitation signal can not stable extremal search system state variable and output valve, and can find out by the partial enlarged drawing of output valve simulation result, there is obvious wave phenomenon in the final convergence result of output valve y.

5, embodiment 5

For the oscillation pressure P in firing chamber in aeromotor _c, its model is:

$\frac{C_c}{A_n}{\stackrel{\&CenterDot;\&CenterDot;}{P}}_c+\frac{\mathrm{\&kappa;}{\mathrm{<figure-callout\; id="2"\; label="C\; c"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">C</figure-callout>}}_c^{}}{2L_n\mathrm{\&rho;}{A}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}\&CenterDot;{\left({\stackrel{\&CenterDot;}{P}}_c\right)}^2+((\frac{\mathrm{\&kappa;}{C}_d{A}_e}{A_n\sqrt{T_4}}+\frac{1}{L_n}-2C_{u}u)+\frac{k_n{C}_n\mathrm{\&kappa;}{C}_d{A}_e}{L_n\mathrm{\&rho;}{A}_n^2\sqrt{T_4}}{P}_c)\&CenterDot;{\stackrel{\&CenterDot;}{P}}_c+\frac{k_n{\mathrm{\&kappa;}}^2{C}_d^2{A}_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{2L_n\mathrm{\&rho;}{A}_n^2{T}_4}\&CenterDot;P_c^2-\frac{k_n\mathrm{\&kappa;}{C}_d{A}_e}{L_n\mathrm{\&rho;}{A}_n^2\sqrt{T_4}}u\&CenterDot;P_c$

$-\frac{1}{A_n}u\&prime;+\frac{k_n}{2L_n\mathrm{\&rho;}{A}_n^2}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">u</figure-callout>}}^2=0---\left(37\right)$

Wherein, C _cthe volume that represents firing chamber; A _nthe cross-sectional area that represents nozzle; κ represents chokes equation constant; L _nthe effective length that represents nozzle; ρ represents nozzle place gas density; C _drepresent coefficient of flow; A _ethe cross-sectional area that represents exit; T ₄the outlet temperature that represents firing chamber; U is the control inputs item of this model, derives from heat and discharges the gas flow causing; k _nrepresent fluid nozzle constant.

The control law of this system is:

$F(V_n,\stackrel{\&OverBar;}{\mathrm{\&phi;}})=\frac{1}{c_p{T}_4}\mathrm{\&rho;}{A}_n{V}_n^s\mathrm{\&Delta;}{H}_s(\stackrel{\&OverBar;}{\mathrm{\&phi;}}+N\&CenterDot;(\frac{{(\frac{V_n^s}{V_n}\stackrel{\&OverBar;}{\mathrm{\&phi;}}-{\mathrm{\&phi;}}_{\mathrm{LB}})}^p\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="e\; p"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{p^{}}{}}\&CenterDot;e^{-{(1-\frac{V_n^s}{V_n}\stackrel{\&OverBar;}{\mathrm{\&phi;}}-\frac{p}{2(1-{\mathrm{\&phi;}}_{\mathrm{LB}})})}^2}}{{(\stackrel{\&OverBar;}{\mathrm{\&phi;}}-{\mathrm{\&phi;}}_{\mathrm{LB}})}^p\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="e\; p"\; filenames="H2008101694813E00032.png,H2008101694813E00041.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{p^{}}{}}\&CenterDot;e^{-{(1-\stackrel{\&OverBar;}{\mathrm{\&phi;}}-\frac{p}{2(1-{\mathrm{\&phi;}}_{\mathrm{LB}})})}^2}}-1))---\left(38\right)$

Wherein, c _pbe illustrated in the specific heat of unit mass gas under fixation pressure;

the nozzle place flow velocity that represents stable state; Δ H _sbe illustrated in the hot release value of burning under certain fuel air ratio; φ represents the average fuel air ratio value of firing chamber, and it is the search variables during burning is controlled; N is scale-up factor, for calculating the stability characteristic (quality) of combustion model; φ _lBrepresent the minimum fuel air ratio under barren fuel, p is a control constant.

The control object of this embodiment is: the limiting control by the average fuel air ratio value φ of firing chamber, makes the oscillation pressure P in firing chamber _chunting range minimize.

Adopt respectively control method that the present invention proposes and self-adaptation control method to the oscillation pressure P in firing chamber in above-mentioned aeromotor _ccarry out limiting control.Simulation result while adopting self-adaptation control method is as shown in Figure 16,17, and the simulation result during control method of employing the present invention proposition, as shown in Figure 18,19, can be found out, although self-adaptation control method is to oscillation pressure P _camplitude have certain inhibiting effect, but do not make P _camplitude converge to a minimum value; And the control method that adopts the present invention to propose makes average fuel air ratio value φ and the oscillation pressure P in firing chamber _camplitude all converge to their minimum value.

Finally it should be noted that, above embodiment is only in order to illustrate the validity of technical scheme of the present invention and this control technology, but be not limited to this, but can extend to other modification, variation, application and embodiment in application, and therefore think that all such modifications, variation, application, embodiment are within the spirit and scope of the present invention.

Claims (7)

1. the neural network extreme control method based on chaos annealing and parameter perturbation, its feature comprises:

Step 10), for extremum search system $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=f(x\left(t\right),u\left(t\right))\\ y=F\left(x\left(t\right)\right)\end{array}\right.,$ X ∈ R wherein ⁿ, u ∈ R ^mwith y ∈ R be respectively the state vector of this system, control vector and output valve, f (x (t), u (t)) be the state equation of this system, F (x (t)) is output function and has a plurality of extreme points, have control law u (t)=β (x (t) θ) stablizes this system, wherein θ=[θ simultaneously ₁, θ ₂..., θ _m] ∈ R ^mthe locating vector of this system, existence function relation during this system stability l:R wherein ^m→ R ⁿbe smooth function, the new output function that obtains this system is y=(F ο l) (θ (t)), take this function as research object, adopts the method for differential differentiate, asks output valve y and locating vector θ time differential variation relation

wherein

the control problem of extremum search system being converted into slope in the output function that solves this system is zero extreme point problem, finally transforms the extreme point problem obtaining and has expression-form

Step 20), according to extreme point Solve problems

adopt duality principle, construct a pair of dual problem with constraint condition, the expression-form of this dual problem is with

wherein $\mathrm{\&upsi;}{\left[\begin{array}{c}{\&PartialD;}^T\left(\mathrm{\&theta;}\right)\\ \left|{\&PartialD;}^T\left(\mathrm{\&theta;}\right)\right|\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)\end{array}\right]}_{3m\&times;1},$ $c={\left[\begin{array}{ccc}{0}_{1\&times;m}& 1_{1\&times;m}& 0_{1\&times;m}\end{array}\right]}^T,$ $M=\left[\begin{array}{ccc}{1}_{1\&times;m}& -\mathrm{sign}(\&PartialD;\left(\mathrm{\&theta;}\right))& 0_{1\&times;m}\\ {\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^T\left(t\right)& 0_{1\&times;m}& 0_{1\&times;m}\\ 0_{1\&times;m}& 0_{1\&times;m}& \&PartialD;\left(\mathrm{\&theta;}\right)\end{array}\right],$ $b=\left[\begin{array}{c}0\\ \stackrel{\&CenterDot;}{y}\left(t\right)\\ \stackrel{\&CenterDot;}{y}\left(t\right)\end{array}\right],$ $\mathrm{sign}\left(\mathrm{\&zeta;}\right)\left\{\begin{array}{cc}1& \mathrm{\&zeta;}>0\\ 0& \mathrm{\&zeta;}=0\\ -1& \mathrm{\&zeta;}<0\end{array}\right.,\mathrm{\&omega;}={\left[\begin{array}{ccc}{\mathrm{\&omega;}}_1& {\mathrm{\&omega;}}_2& {\mathrm{\&omega;}}_3\end{array}\right]}_{3\&times;1}^T$ For the dual variable of υ, meeting p ₁(υ)=0 and p ₂(ω), under=0 constraint condition, make g simultaneously ₁(υ) minimize and g ₂(ω) maximize;

Step 30), according to this dual problem

with

utilization has the neural network of parameter perturbation, and its mathematical form is $\left\{\begin{array}{c}\frac{{\mathrm{du}}_1}{\mathrm{dt}}=-\mathrm{\&mu;}[D\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]\\ \frac{{\mathrm{du}}_2}{\mathrm{dt}}=-\mathrm{\&mu;}[-D\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]\\ \mathrm{\&upsi;}=\frac{1}{1+\exp (-u_1/{\mathrm{\&epsiv;}}_1)}-0.5\\ \mathrm{\&omega;}=\frac{1}{1+\exp (-u_2/{\mathrm{\&epsiv;}}_2)}-0.5\end{array}\right.,$ Using the output valve y of this extremum search system as the input quantity with the neural network of parameter perturbation, and υ and ω be as the output quantity of this neural network, and at the state variable u of this neural network ₁and u ₂expression formula in adopt stacked system to introduce chaotic noise χ ₁and χ ₂, obtain new state variable u ₁and u ₂expression formula is $\left\{\begin{array}{c}\frac{{\mathrm{du}}_1}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[D_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]+{\mathrm{\&Gamma;}}_1({\mathrm{\&chi;}}_1({\mathrm{\&tau;}}_1-{\mathrm{\&rho;}}_1)+{\mathrm{\&rho;}}_1)& \mathrm{randnum}<P_1\left(t\right)\\ -\mathrm{\&mu;}[D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]& \mathrm{otherwise}\end{array}\right.\\ \frac{{\mathrm{du}}_2}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[-D_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]+{\mathrm{\&Gamma;}}_2({\mathrm{\&chi;}}_2({\mathrm{\&tau;}}_2-{\mathrm{\&rho;}}_2)+{\mathrm{\&rho;}}_2)& \mathrm{randnum}<P_2\left(t\right)\\ -\mathrm{\&mu;}[-D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]& \mathrm{otherwise}\end{array}\right.\end{array}\right.,$ Chaotic noise χ wherein ₁and χ ₂be to be produced by Lorenz model, its mathematical form is $\left\{\begin{array}{c}\frac{{\mathrm{d\&chi;}}_1}{\mathrm{dt}}=a_a({\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1)\\ \frac{{\mathrm{d\&chi;}}_2}{\mathrm{dt}}=b_b{\mathrm{\&chi;}}_1-{\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_3\\ \frac{{\mathrm{d\&chi;}}_3}{\mathrm{dt}}={\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_2-c_c{\mathrm{\&chi;}}_3\end{array}\right.,$ Parameter a wherein _a=10, b _b=28 thereby set up a kind of neural network extreme control method based on chaos annealing and parameter perturbation, the concrete mathematical expression form of the method is as follows:

$\frac{{\mathrm{du}}_1}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[D_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]+{\mathrm{\&Gamma;}}_1({\mathrm{\&chi;}}_1({\mathrm{\&tau;}}_1-{\mathrm{\&rho;}}_1)+{\mathrm{\&rho;}}_1)& \mathrm{randnum}<P_1\left(t\right)\\ -\mathrm{\&mu;}[D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_1\left(\mathrm{\&upsi;}\right)}{\&PartialD;\mathrm{\&upsi;}}\&CenterDot;p_1\left(\mathrm{\&upsi;}\right)]& \mathrm{otherwise}\end{array}\right.$

$\frac{{\mathrm{du}}_2}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&mu;}[-D_1\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]+{\mathrm{\&Gamma;}}_2({\mathrm{\&chi;}}_2({\mathrm{\&tau;}}_2-{\mathrm{\&rho;}}_2)+{\mathrm{\&rho;}}_2)& \mathrm{randnum}<P_2\left(t\right)\\ -\mathrm{\&mu;}[-D_2\left(t\right)\&CenterDot;\frac{{\&PartialD;g}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;(g_1\left(\mathrm{\&upsi;}\right)-g_2\left(\mathrm{\&omega;}\right))+\frac{{\&PartialD;p}_2\left(\mathrm{\&omega;}\right)}{\&PartialD;\mathrm{\&omega;}}\&CenterDot;p_2\left(\mathrm{\&omega;}\right)]& \mathrm{otherwise}\end{array}\right.$

D ₁(t)=C

D ₂(t)=γα ^-ηt

$\mathrm{\&upsi;}=\frac{1}{1+\exp (-u_1/{\mathrm{\&epsiv;}}_1)}-0.5$

$\mathrm{\&omega;}=\frac{1}{1+\exp (-u_2/{\mathrm{\&epsiv;}}_2)}-0.5$

$\frac{{\mathrm{d\&Gamma;}}_i\left(t\right)}{\mathrm{dt}}=\left\{\begin{array}{cc}-\mathrm{\&kappa;}& {\mathrm{\&Gamma;}}_i\left(t\right)>0\\ 0& \mathrm{otherwise}\end{array}\right.,i=\mathrm{1,2}$

$P_1\left(t\right)=\exp [-\left(\frac{{\mathrm{\&upsi;}}^{\&prime;}}{K_{B}T}\right)]$

$P_2\left(t\right)=\exp [-\left(\frac{{\mathrm{\&omega;}}^{\&prime;}}{K_{B}T}\right)]$

$\left\{\begin{array}{c}\frac{{\mathrm{d\&chi;}}_1}{\mathrm{dt}}=a_a({\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1)\\ \frac{{\mathrm{d\&chi;}}_2}{\mathrm{dt}}{=b}_b{\mathrm{\&chi;}}_1-{\mathrm{\&chi;}}_2-{\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_3\\ \frac{{\mathrm{d\&chi;}}_3}{\mathrm{dt}}={\mathrm{\&chi;}}_1{\mathrm{\&chi;}}_2-c_c{\mathrm{\&chi;}}_3\end{array}\right.$

$T=\frac{T_0}{\ln (h+t)}$

Wherein, the output valve y of extremum search system is as the input quantity of this neural network, and υ and ω are as the output quantity of this neural network, P ₁and P (t) ₂(t) represent respectively chaotic noise χ ₁and χ ₂acceptance probability, and P all the time ₁(t)>=0 and P ₂(t)>=0,

k _bbe Boltzmann constant, T is annealing temperature, T ₀be initial annealing temperature and h > 1, parameter randnum is illustrated in [r _a, 1] between random number, r _a∈ [0,1] is lowest confidence, Γ ₁and Γ (t) ₂(t) be respectively chaotic noise χ ₁and χ ₂influence coefficient, and Γ all the time ₁(t)>=0 and Γ ₂(t)>=0, κ (0 < κ < 1) is influence coefficient Γ ₁and Γ (t) ₂(t) decay factor, ε ₁> 0 and ε ₂> 0 is the gain coefficient of output vector υ and ω, and parameter a _a=10, b _b=28,

[τ ₁, ρ ₁] and [τ ₂, ρ ₂] be chaos state χ ₁and χ ₂the scope of space, state variable u while selecting its size to meet this neural network not introduce chaos annealing ₁and u ₂10% of maximum rate of change, and symmetrical about zero point, C is normal number;

Step 40), by the solving of the described neural network extreme control method based on chaos annealing and parameter perturbation, obtain the search variables θ of global optimum of this extremum search system ^*;

Step 50), according to the search variables θ of global optimum of gained ^*, the output valve y that orders about this extremum search system converges to the global extremum point y of output function ^*thereby, realize the control object of extremum search system.

2. according to the method for claim 1, obtain a kind of neural network extreme control system based on chaos annealing and parameter perturbation, its feature comprises: model emulation pattern and real-time control mode, wherein, model emulation pattern is for definite neural network extreme control method based on chaos annealing and parameter perturbation, to regulate the mode unit of parameter, and real-time control mode is the mode unit for extremum search system on line real time control.

3. the system of claim 2, wherein, global search and the control ability of the neural network extreme control method of model emulation model validation based on chaos annealing and parameter perturbation in different extreme value search systems and various function optimization problem.

4. the system of claim 2, wherein, real-time control mode is accepted the measured signal of extremum search controlled system by feedback, the neural network extreme control method of utilization based on chaos annealing and parameter perturbation, calculate in real time corresponding control signal, for controlling the output valve asymptotic convergence of extremum search system to the global extremum point of output function.

5. the system of claim 2, wherein, described model emulation pattern and real-time control mode not only have limiting control ability to the extremum search system of having preserved, and can expand and accept new extremum search system model, and it is carried out to limiting control.

6. the system of claim 2, wherein, the real-time extremum search control system consisting of described real-time control mode further comprises: multichannel sensor mechanism, data acquisition module, digital signal driving mechanism, digital-to-analog conversion mechanism, voltage and power amplifier and topworks.

7. the system of claim 6, wherein, the multichannel sensor mechanism in described real-time extremum search control model can measure and comprise: the various states signals such as temperature, pressure, distance, rotating speed, angle; Data acquisition module comprises analog-to-digital conversion function.

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