CN103324093B - A kind of multi-model Adaptive Control system and control method thereof - Google Patents

Abstract

The invention discloses a kind of multi-model Adaptive Control system, control for the nonlinear discrete time system of a class Bounded Linear, including linear robust adaptive controller, nonlinear neural network adaptive controller and switching mechanism, this switching mechanism connects two adaptive controllers and the input of controlled device respectively, and two adaptive controllers connect the outfan of controlled device；Linear robust adaptive controller includes linear robust adaptive model and linear robust controller, and nonlinear neural network adaptive controller includes nonlinear neural network adaptive model and nonlinear neural network controller；The input of controlled device is selected by switching construction to produce between the two controllers, and it is provided with a close loop negative feedback between the output of controlled device and two adaptive controllers, for subtracting each other relation between the model output of controlled device and two adaptive controllers, thus calculate model error, for adjusting the parameter of model and the weights of neutral net.

Description

A kind of multi-model Adaptive Control system and control method thereof

Technical field

The present invention relates to Self Adaptive Control field, particularly relate to a kind of multi-model Adaptive Control system and control method thereof.

Background technology

Existing major part real system is all nonlinear system, is generally of model structure uncertain, unknown parameters, the features such as Parameters variation is frequent；Self Adaptive Control can carry out on-line identification to nonlinear system, utilizes the systematic parameter that identification obtains to design controller；This method can be widely applied to the control of nonlinear system, but, when the uncertainty of system is the biggest, the change of such as operating condition, it is bad or lose the situation of stability that the self-adaptation control method of the single identifier of tradition is likely to occur transient performance.

The proposition of multi-model Adaptive Control method, solves this problem by comprising following two parts: 1) multi-controller, it is made up of multiple identifiers and candidate's controller, multiple identifiers can cover whole parameter space；2) switching mechanism, by selecting candidate's controller to produce control input；Research to multi-model automatic correction controling method at present is mainly concentrated in optimizing multi-model collection, reduces Models Sets scale, reaches to improve the purpose controlling response speed；And how designing switching mechanism so that multi-model self-aligning control system has more preferable transient performance and robust performance.

Non-linear controlled device be there are certain requirements by multi-model automatic correction controling method, thus meet stability and the robustness of nonlinear control system, this has had a strong impact on the method extensive application in practice, and in terms of relaxing the assumed condition to controlled device, achievement is less；Initially, nonlinear system is carried out linearisation, system is divided into linear segment and nonlinear high-order function item, it is desirable to nonlinear terms are bounded, and nonlinear system is minimum phase system；By the introducing of k difference operator, nonlinear terms bounded is loosened to the rate of rise bounded of nonlinear terms；On the basis of nonlinear terms rate of rise bounded, generalized minimum-variance adaptive controller is introduced into, and above-mentioned conclusion is generalized to non-minimum phase system；But these conditions are still the strictest for the requirement of nonlinear system, need to relax further.

Therefore, we must propose a kind of multi-model neural network self-adaptation control method relating to a class Bounded Linear non-linear complax control system, to solve in prior art the impact of the restrictive condition etc. on nonlinear system.

Summary of the invention

In order to overcome the defect of prior art, it is desirable to provide a kind of restrictive condition that can relax nonlinear system, and expand a kind of multi-model Adaptive Control system and the control method thereof of the range of multi-model Adaptive Control method.

To achieve these goals, the invention provides a kind of multi-model Adaptive Control system, control for the nonlinear discrete time system of a class Bounded Linear, including two Indirect adaptive control devices and switching mechanism, described switching mechanism connects said two Indirect adaptive control device and the input of a controlled device respectively, and said two Indirect adaptive control device connects the outfan of described controlled device；It is provided with between outfan and the said two Indirect adaptive control device of described controlled device between a close loop negative feedback, and the model output of described controlled device and said two Indirect adaptive control device and is set to subtract each other relation；The input of described controlled device is selected to produce by described switching mechanism between said two Indirect adaptive control device, thus computation model error, for adjusting the parameter of said two model and the weights of neutral net.

It is preferred that said two Indirect adaptive control device includes linear robust adaptive controller and nonlinear neural network adaptive controller.

It is preferred that described linear robust adaptive controller includes linear robust adaptive model and linear robust controller；Described linear robust adaptive model is by projection identification algorithm, it is ensured that when the restrictive condition of the nonlinear terms of described multi-model Adaptive Control system is loosened to Bounded Linear, the Identification Errors also bounded of described linear robust adaptive model.

Preferably, described linear robust controller is linear pole-placement and adaptive control device, by described linear pole-placement and adaptive control device by the Assignment of Closed-Loop Poles of described multi-model Adaptive Control system to desired locations, thus obtain the ability of the control problem processing non-minimum phase system and open-loop unstable system.

Preferably, described nonlinear neural network adaptive controller includes nonlinear neural network adaptive model and nonlinear neural network controller, and described nonlinear neural network adaptive model is grouped into by linear segment and non-linear, the coefficient of described linear segment is updated as auto-adaptive parameter, and described non-linear partial is made up of neutral net；The described nonlinear neural network adaptive model weights by on-line tuning neutral net, thus obtain the estimation to described controlled device and export.

It is preferred that described nonlinear neural network controller is the pole-placement and adaptive control device with nonlinear terms, improved the control accuracy of described multi-model Adaptive Control system by the described pole-placement and adaptive control device with nonlinear terms.

It is preferred that described switching mechanism is provided with performance indications module, and described performance indications module includes cumulative error part and model error part, and described cumulative error part is for preventing the frequent switching of described multi-model Adaptive Control system；Described switching mechanism by calculating the performance indications of each controller in each control moment, thus selects the controller that performance indications are less to produce the control input of subsequent time.

The invention allows for a kind of multi-model Adaptive Control method, comprise the steps:

S1: system initialization: random initializtion linear robust adaptive model and the parameter of nonlinear neural network adaptive model, and the weights of random initializtion neutral net；

In the S2:k=0 moment, controlled device is output as 0；When k ≠ 0 moment, controlled device is output as the real output value of system, makees difference with the setting value of system and obtains the control error e of system_c, the real output value of system obtains model error e with the output work difference of linear robust adaptive model₁, the real output value of system and nonlinear neural network adaptive model are made difference and are obtained model error e₂；

S3: be utilized respectively the parameter of the parameter computing controller of two models, error e will be controlled_cAs linear robust controller and the input of nonlinear neural network controller, two controllers produce controlled quentity controlled variable u respectively₁And u₂；

S4: calculate linear robust controller and the performance index value of nonlinear neural network controller, and select the input u that the controller that performance index value is less produces_i, as the control input u of controlled device and linear robust adaptive model and nonlinear neural network adaptive model；

S5: update linear robust adaptive model and the parameter of nonlinear neural network adaptive model and the weights of neutral net respectively；

S6: forward step S2 to.

It is preferred that described neutral net is set to single hidden layer, and the number of the hidden neuron of described neutral net is usually arranged as 6-10.

Compared with prior art, beneficial effects of the present invention is as follows:

1, the present invention be can be seen that by multi-model Adaptive Control method, linear robust adaptive controller comprises a linear robust adaptive model, this linear robust adaptive model is by introducing the projection identification algorithm with standardized correction, the restrictive condition of the nonlinear terms of controlled device is loosened to Bounded Linear, greatly widens the scope of application of multi-model Adaptive Control system.

2, the present invention is by arranging pole-placement and adaptive control device, by the Assignment of Closed-Loop Poles of multi-model Adaptive Control system to desired position, the requirement of the performance indications etc. to closed loop system is embodied by providing limit, use pole-placement and adaptive control device to can ensure that the stability of non-minimum phase system, thus the restrictive condition of controlled device is loosened to non-minimum phase system from minimum phase system.

3, the present invention design by switching mechanism, the controller making multi-model Adaptive Control system switches between linear Robust adaptive controller and nonlinear neural network adaptive controller, and selects controller that performance index value is less to input as the control of current system；And performance indications comprise the accumulation item of an error so that system output is the most smooth；And owing to linear robust adaptive control system has stability, and the present invention uses linear robust adaptive controller and nonlinear neural network adaptive controller to switch over, so that the multi-model Adaptive Control system of the present invention has stability.

Accompanying drawing explanation

The multi-model Adaptive Control device that Fig. 1 designs for the present invention close feedback control system block diagram；

Fig. 2 is linear robust adaptive controller structure chart of the present invention；

Fig. 3 is nonlinear neural network adaptive controller structure chart of the present invention;

Fig. 4 is the structure chart of neutral net of the present invention；

Fig. 5 is the switching flow figure of switching mechanism of the present invention；

Fig. 6 is the simulation experiment result figure.

Symbol list:

M₁-linear robust adaptive model, M₂-nonlinear neural network adaptive model, C₁-linear robust controller, C₂-nonlinear neural network controller, 100-switching mechanism, 200-controlled device.

Detailed description of the invention:

See the accompanying drawing illustrating the embodiment of the present invention, the present invention hereafter be will be described in greater detail.But, the present invention can in different forms, specification etc. realizes, and should not be construed as the embodiment by herein proposing and limited.On the contrary, proposing these embodiments is to reach fully and complete disclosure, and makes more relevant those skilled in the art understand the scope of the present invention completely.In these accompanying drawings, for clearly visible, relative size may be zoomed in or out.

The multi-model Adaptive Control system implemented according to the present invention is described in detail referring now to Fig. 1, this multi-model Adaptive Control system is multi-model Adaptive Control system and the control method thereof of a class Bounded Linear nonlinear system, relax the restrictive condition of nonlinear system, thus expand the range of multi-model Adaptive Control method.This multi-model Adaptive Control system is made up of a linear robust adaptive controller, a neutral net Indirect adaptive control device and a switching mechanism；Wherein this switching mechanism one end connects the input of controlled device, and the other end connects linear Robust adaptive controller and neutral net Indirect adaptive control device respectively；This linear robust adaptive controller and neutral net Indirect adaptive control device are connected with controlled device respectively, and two be provided with a close loop negative feedback between controller and controlled device, and be set to subtract each other relation between the model output of controlled device and two controllers, thus calculate model error, and this model error is for adjusting the parameter of model and the weights of neutral net.

Wherein, linear robust adaptive controller includes linear robust adaptive model and linear robust controller, linear segment after linear robust adaptive model correspondence multi-model Adaptive Control system linearization, it it is a kind of linear autoregression moving average input/output model, adaptive parameter is the coefficient of linear regression vector, adaptive law uses standardized correction of band to project identification algorithm, according to determining that equivalence principle utilizes identified parameters to design Pole Assignment Controller, by projection identification algorithm, ensure when the restrictive condition of the nonlinear terms of multi-model Adaptive Control system is loosened to Bounded Linear, the Identification Errors of linear robust adaptive model also bounded.And, linear robust controller is linear pole-placement and adaptive control device, by pole-placement and adaptive control device by the Assignment of Closed-Loop Poles of multi-model Adaptive Control system to desired locations, thus obtain the ability of the control problem processing non-minimum phase system and open-loop unstable system.

And, nonlinear neural network adaptive controller includes nonlinear neural network adaptive model and nonlinear neural network controller, the nonlinear neural network adaptive model weights by on-line tuning neutral net, it is thus achieved that the estimation to controlled device exports；Nonlinear neural network adaptive model is grouped into by linear segment and non-linear, the coefficient of linear segment can be updated in any way as auto-adaptive parameter, non-linear partial is made up of neutral net, and this neutral net uses BP neutral net, error back propagation method is utilized to train, and according to determining equivalence principle, the neural network model utilizing identified parameters with obtaining, designs non-linear pole-placement and adaptive control device；The control accuracy of multi-model Adaptive Control system is improved by non-linear pole-placement and adaptive control device.

It addition, switching mechanism is provided with performance indications module, and performance indications module includes cumulative error part and model error part, and cumulative error part is for preventing the frequent switching of multi-model Adaptive Control system；Switching mechanism by calculating the performance indications of each controller in each control moment, thus selects the controller that performance indications are less to produce the control input of subsequent time.

The invention allows for a kind of multi-model Adaptive Control method, comprise the steps:

S1: system initialization: random initializtion linear robust adaptive model and the parameter of nonlinear neural network adaptive model, and the weights of random initializtion neutral net；

In the S2:k=0 moment, controlled device is output as 0；When k ≠ 0 moment, controlled device is output as the real output value of system, makees difference with the setting value of system and obtains the control error e of system_c, the real output value of system obtains model error e with the output work difference of linear robust adaptive model₁, the real output value of system and nonlinear neural network adaptive model are made difference and are obtained model error e₂；

S3: be utilized respectively the parameter of the parameter computing controller of two models, error e will be controlled_cAs linear robust controller and the input of nonlinear neural network controller, two controllers produce controlled quentity controlled variable u respectively₁And u₂；

S4: calculate linear robust controller and the performance index value of nonlinear neural network controller, and select the input u that the controller that performance index value is less produces_i, as the control input u of controlled device and linear robust adaptive model and nonlinear neural network adaptive model；

S5: update linear robust adaptive model and the parameter of nonlinear neural network adaptive model and the weights of neutral net respectively；

S6: forward step S2 to.

Wherein, neutral net is set to single hidden layer, and the number of the hidden neuron of neutral net is usually arranged as 6-10.

Application examples

As shown in Figure 1, in the controller designed by multi-model Adaptive Control method of the present invention, it is made up of a linear robust adaptive controller, a nonlinear neural network adaptive controller and a switching mechanism.In figure, r (k+n) is the tracking reference signal of multi-model Adaptive Control system, u_pK () is the input of controlled device, y_p(k+n) it is the output of controlled device；Linear robust adaptive controller comprises linear robust adaptive model M₁With linear pole-placement and adaptive control device C₁, u₁K () is linear pole-placement and adaptive control device C₁Output, y_p(k+n) it is linear robust adaptive model M₁Output；Nonlinear neural network adaptive controller comprises nonlinear neural network adaptive model M₂With non-linear pole-placement and adaptive control device C₂, u₂K () is non-linear pole-placement and adaptive control device C₂Output, y₂(k+n) it is nonlinear neural network adaptive model M₂Output.u_p(k) by switching mechanism at u₁(k) and u₂Select between (k) to produce.

Nonlinear system for constant during following input/output format discrete:

$y_p(k+n)=-\underset{j=0}{\overset{n-1}{\mathrm{\Σ}}}{a}_j{y}_p(k+j)+\underset{j=0}{\overset{M}{\mathrm{\Σ}}}{b}_j{u}_p(k+j)+f\left(w\left(k\right)\right)$

$=\mathrm{\θw}\left(k\right)+f\left(w\left(k\right)\right)---\left(1\right)$

θ=[θ in formula_a,θ_b], θ_a=[a_n-1,a_n-2,…,a₀]^T,θ_b=[b_m,b_m-1,…,b₀]^T,w(k)=[-y_p(k+n-1),…,-y_p(k),u_p(k+m),…,u_p(k)]^T。

Make α_n=[zⁿ,…,z,1], $A(z,k)=z^n+{\mathrm{\θ}}_a^T{\mathrm{\α}}_{n-1}=z^n+a_{n-1}{z}^{n-1}+\·\·\·+a_0,$ $B(z,k)={\mathrm{\θ}}_b^T{\mathrm{\α}}_m=b_m{z}^m$ $+b_{m-1}{z}^{m-1}+\·\·\·+b_0,$ Then system can be expressed as:

A(z,k)y_p(k)=B(z,k)u_p(k)+f(w(k)) (2)

System (1) both sides are filtered, Λ_pFor the Hurwitz multinomial that order is n, its root all existsRegion in, 0≤δ₀<1。

$\frac{z^n{y}_p\left(k\right)}{{\mathrm{\&Lambda;}}_p}={\mathrm{\&theta;}}^T\frac{w\left(k\right)}{{\mathrm{\&Lambda;}}_p}+\frac{f\left(w\left(k\right)\right)}{{\mathrm{\&Lambda;}}_p}---\left(3\right)$

Order $\mathrm{\&zeta;}=\frac{z^n{y}_p\left(k\right)}{{\mathrm{\&Lambda;}}_p},\mathrm{\&phi;}\left(k\right)=\frac{w\left(k\right)}{{\mathrm{\&Lambda;}}_p},\mathrm{\&eta;}\left(k\right)=\frac{f\left(w\left(k\right)\right)}{{\mathrm{\&Lambda;}}_p},$ Then system (1) can be write as

ζ(k)=θ^Tφ(k)+η(k) (4)

System (3) is given hypothesis below:

Assume 1: order n is known for system, and m≤n-1；

Assume 2: assume | η (k) |≤μ | | φ (k) | |+γ, μ > 0, γ > 0；

Assume 3: θ ∈ Ω,It is to compact known to one.

By linear robust Indirect adaptive control structure chart shown in accompanying drawing 2, this controller includes linear robust adaptive model and linear pole-placement and adaptive control device two parts composition, sets up system linearity robust adaptive model M₁:

${\widehat{\mathrm{\&zeta;}}}_1\left(k\right)={\mathrm{\&theta;}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)---\left(5\right)$

θ in formula₁(k)=[b_1,0(k),…,b_1,m(k),a_1,0(k),…,a_1,n-1(k)]^T, it is model M₁Parameter in the k moment.

According to assuming 3, a N can be obtained₀> 0 so that all θ ∈ Ω are hadModel M₁Parameter use following projection identification algorithm be updated, whereinIt is θ₁The identification of (t):

${\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)={\widehat{\mathrm{\&theta;}}}_1(k-1)+{\mathrm{\&Gamma;}}_1{\mathrm{\&epsiv;}}_1\mathrm{\&phi;}\left(k\right),{\mathrm{\&theta;}}_1\left(0\right)\&Element;\mathrm{\&Omega;}---\left(6\right)$

${\widehat{\mathrm{\&theta;}}}_1\left(k\right)=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& \mathrm{if}\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|\&le;N_0\\ \frac{N_0}{\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& \mathrm{otherwise}\end{array}\right.---\left(7\right)$

${\mathrm{\&epsiv;}}_1\left(k\right)=\frac{\mathrm{\&zeta;}\left(k\right)-{\widehat{\mathrm{\&theta;}}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)}{m_s^2\left(k\right)}---\left(8\right)$

$m_s^2\left(k\right)={(\mathrm{\&tau;}+|\left|\mathrm{\&phi;}\left(k\right)\right|\left|\right)}^2+n_d\left(k\right)---\left(9\right)$

n_d(k+1)=δ₀n_d(k)+|u_p(k)|²+|y_p(k)|² (10)

In formula,n_d(0)=0,0<Γ₁<2,ε₁It it is standardized model error.

Make θ₁=[θ_1a,θ_1b],θ_1a=[a_1,n-1,a_1,n-2,…,a_1,0]^T,θ_1b=[b_1,m,b_1,m-1,…,b_1,0]^T,

${\hat{A}}_1(z,k)=z^n+{\mathrm{\&theta;}}_{1a}{\mathrm{\&alpha;}}_{n-1},$ ${\hat{B}}_1(z,k)={\mathrm{\&theta;}}_{1b}{\mathrm{\&alpha;}}_m.$

Linear pole-placement and adaptive control device C is designed according to linear robust adaptive model₁:

${\hat{L}}_1(z,k)Q_m\left(z\right)u_1\left(k\right)=-{\hat{P}}_1(z,k)(y_p\left(k\right)-y_m\left(k\right))---\left(11\right)$

Determined by following formulaWith

${\hat{A}}_1(z,k){\hat{L}}_1(z,k)Q_m\left(z\right)+{\hat{P}}_1(z,k){\hat{B}}_1(z,k)=A^{*}\left(z\right)---\left(12\right)$

In formula ${\hat{L}}_1(z,k)=z^{n-1}+{{\stackrel{\&OverBar;}{l}}_1}^T{\mathrm{\&alpha;}}_{n-2},{\hat{P}}_1(z,k)=p_{10}{z}^{n+q-1}+{{\stackrel{\&OverBar;}{p}}_1}^T{\mathrm{\&alpha;}}_{n+q-2},$ A^*Z () is the closed loop proper polynomial of Hurwitz.

By nonlinear neural network adaptive controller structure chart shown in accompanying drawing 3, this controller includes nonlinear neural network adaptive model M₂With non-linear pole-placement and adaptive control device C₂Two parts.

Set up neural network model M₂:

${\widehat{\mathrm{\&zeta;}}}_2\left(k\right)={\mathrm{\&theta;}}_2^T(k-1)\mathrm{\&phi;}\left(k\right)+\widehat{\mathrm{\&eta;}}(W\left(k\right),k)---\left(13\right)$

Being that the nonlinear function of the bounded of Neural Networks Representation approaches, W (k) is the weight coefficient of neutral net, updates by error back propagation method.

θ₂K () utilizes the projection identification algorithm revised to determine,It is θ₂The identification of (t):

${\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_2\left(k\right)={\widehat{\mathrm{\&theta;}}}_2(k-1)+{\mathrm{\&Gamma;}}_2{\mathrm{\&epsiv;}}_2\mathrm{\&phi;}\left(k\right),{\widehat{\mathrm{\&theta;}}}_2\left(0\right)\&Element;\mathrm{\&Theta;}---\left(14\right)$

${\widehat{\mathrm{\&theta;}}}_2\left(k\right)=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_2\left(k\right)& \mathrm{if}\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_2\left(k\right)\right|\&le;N_0\\ \frac{N_0}{\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_2\left(k\right)\right|}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_2\left(k\right)& \mathrm{otherwise}\end{array}\right.---\left(15\right)$

${\mathrm{\&epsiv;}}_2\left(k\right)=\frac{\mathrm{\&zeta;}\left(k\right)-{\widehat{\mathrm{\&theta;}}}_2^T(k-1)\mathrm{\&phi;}\left(k\right)-\widehat{\mathrm{\&eta;}}(W\left(k\right),k)}{m_s^2\left(k\right)}---\left(16\right)$

$m_s^2\left(k\right)={(\mathrm{\&tau;}+|\left|\mathrm{\&phi;}\left(k\right)\right|\left|\right)}^2+n_d\left(k\right)---\left(17\right)$

n_d(k+1)=δ₀n_d(k)+|u_p(k)|²+|y_p(k)|² (18)

In formula,n_d(0)=0,0<Γ₂<2,ε₂It it is standardized model error.

Order

θ_2a=[a_2,n-1,a_2,n-2,…,a_2,0]^Tθ_2b=[b_2,m,b_2,m-1,…,b_2,0]^T

${\hat{B}}_2(z,k)={\mathrm{\&theta;}}_{2b}{\mathrm{\&alpha;}}_m.$

According to nonlinear neural network adaptive model M₂, the non-linear pole-placement and adaptive control device C of available system₂:

${\hat{L}}_2(z,k)Q_m\left(z\right)u_2\left(k\right)=-{\hat{P}}_2(z,k)(y_p\left(k\right)-y_m\left(k\right))+F\left(z\right)\widehat{\mathrm{\&eta;}}(W\left(k\right),k)---\left(19\right)$

F (z) is feedback oscillator, following formula determineWith

${\hat{A}}_2(z,k){\hat{L}}_2(z,k)Q_m\left(z\right)+{\hat{P}}_2(z,k){\hat{B}}_2(z,k)=A^{*}\left(z\right)---\left(20\right)$

In formula ${\hat{L}}_2(z,k)=z^{n-1}+{{\stackrel{\&OverBar;}{l}}_2}^T{\mathrm{\&alpha;}}_{n-2},{\hat{P}}_2(z,k)=p_{20}{z}^{n+q-1}+{\stackrel{\&OverBar;}{p}}_2^T{\mathrm{\&alpha;}}_{n+q-2}.$

Structure chart by neutral net shown in accompanying drawing 4, this neutral net is the BP neutral net including these three layers of neurons of input layer, hidden layer and output layer, each neuron between levels connects entirely, does not connect between every layer of neuron, and the connection weight of input layer to intermediate layer is l_ij,i=1,2,…,n_a+n_b-2,j=1,2,…,p；Hidden layer is v to the connection weight of output layer_j1,j=1,2,…,p；Hidden layer each unit output threshold value is τ_j,j=1,2,…,p；The output threshold value of output layer unit is γ₁；Parameter k=1,2 ..., m, input as w (k)=[-y_p(k+n-1),…,-y_p(k),u_p(k+m),…,u_p(k)]^T。

The input s of each neuron of hidden layer_jFor:Use s_jThe output b of each neuron of hidden layer is calculated by transferometer_jFor: b_j=g(s_j), j=1,2 ..., p. utilizes the output b of hidden layer_j, connection weight v_j1And threshold gamma₁Calculate the output L of output layer neuron_tFor:Then the response of output layer neuron is calculated by transferometerFor:Utilize connection weight v_j1, error e₂(k), and the output b of hidden layer_j, calculate error d of each neuron of hidden layer_j(t)。

d_j(k)=[e₂(k)v_j1]b_j(1-b_j) (21)

Utilize output error e₂The output b of (k) and each neuron of hidden layer_jRevise connection weight v_j1And threshold gamma₁:

v_j1=v_j1+κe₂(k)b_j

γ₁=γ₁+κe₂(k)

j=1,2,L,p,0<κ<1

Utilize error d of hidden neuron_j(k), input w (k) of input layer=[-y_p(k+n-1),…,-y_p(k),u_p(k+m),…,u_p(k)]^TRevise connection weight l_ijAnd threshold tau_j:

l_ij=l_ij+σd_j(k)w_i(k)

τ_j=τ_j+σd_j(k)

i=1,2,…,n_a+n_b-2,j=1,2,…,p,0<σ<1.

Shown in the flow chart of the switching mechanism of accompanying drawing 5, first separately design performance indications J for linear robust Indirect adaptive control and nonlinear neural network Indirect adaptive control₁(k) and J₂(k), its computational methods are as follows:

$J_i\left(k\right)=\underset{l=1}{\overset{k}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Gamma;}}_0}{2}{\mathrm{\&epsiv;}}_i^2\left(l\right)+c\underset{l=k-N+1}{\overset{k}{\mathrm{\&Sigma;}}}{e}_i^2\left(l\right),i=\mathrm{1,2}---\left(22\right)$

E in formula_i(k)=ε_im_s, Γ₀> 0, c >=0 is the constant of definition.

At each system time, calculate J respectively₁And J₂Value, controller switching signal $\mathrm{\&sigma;}\left(k\right)=\left\{\begin{array}{cc}1& J_1\left(k\right)\&le;J_2\left(k\right)\\ 2& J_1\left(k\right)>J_2\left(k\right)\end{array}\right..$

Multi-model self tuning controller C is defined as:

u_p(k)=u_{σ (k)} (23)

Accompanying drawing 6 is multi-model Adaptive Control system experimentation result of the present invention, "-" multi-model Adaptive Control of the present invention device in Fig. 6 (a), and "--" is linear robust adaptive controller, and ". " is reference signal；The output valve at different time of different controlling value is can be seen that from figure；In Fig. 6 (b), vertical coordinate is that switching construction switches selective value, and wherein 1 represents that switching mechanism selects linear robust adaptive controller as controlling output；2 represent that switching mechanism selects nonlinear neural network adaptive controller as controlling output.

From the discussion above, the multi-model Adaptive Control method of the present invention to be embodied as On-line Control step as follows:

S1: system initialization: random initializtion linear robust adaptive model M₁With nonlinear neural network adaptive model M₂Parameter and the weights of neutral net, can determine according to priori；

In the S2:k=0 moment, system is output as zero, i.e. y (0)=0；When k ≠ 0 moment, the controlled device of system provide the true output y of system_pK (), by model M₁And M₂Provide the estimation output y of model respectively₁(k) and y₂(k)；

$y_1(k+1)={{\widehat{\mathrm{\&theta;}}}_1}^T\left(k\right)\mathrm{\&psi;}\left(k\right)$

$y_2(k+1)={{\mathrm{\&theta;}}_2}^T\left(k\right)w\left(k\right)+f_2(W\left(k\right),\stackrel{\&OverBar;}{w}\left(k\right))$

The estimation difference of S3: computation model is respectively e₁(k)=y(k)-y₁(k) and e₂(k)=y(k)-y₂(k)；

S4: calculated the control error e of system by the y (k) that truly exports of reference input r (k) of system and system_c(k)；

S5: utilize model M₁And M₂Parameter design controller C₁And C₂Parameter, according to formula (5) (8), by the control error e of system_cK () calculates linear robust controller and output valve u of nonlinear neural network controller respectively₁(k) and u₂(k)；

S6: calculated performance indications J of each controller by model estimation difference₁(k) and J₂(k)；

S7: the controller u less by the value of switching mechanism formula (11) selection performance indications_iK () inputs u as the control of controlled device_p(k)；

S8: by model estimation difference e₁(k) and e₂K (), according to respective adaptive law (6) and (14), updates linear robust adaptive model M respectively₁With nonlinear neural network adaptive model M₂Parameter and the weights of neutral net；

S9: return to step S2.

The Indirect adaptive control device that the present invention provides is not limited in linear robust adaptive controller and the nonlinear neural network adaptive controller that the present embodiment proposes, it is also possible to includes other nonlinear autoregressive devices, thus realizes multi-model Adaptive Control；And the neutral net that the present invention proposes is not limited with this BP neutral net proposed, and the number of the hidden neuron of neutral net be also not limited to the present embodiment propose number be limited, may be arranged as the neutral net of other numbers of plies, it is thus possible to train according to Back Propagation Algorithm, and the BP neutral net that the present embodiment proposes is only a wide variety of neural network model.

Obviously, those skilled in the art can carry out various change and deform without departing from the spirit and scope of the present invention the present invention.So, if these amendments of the present invention and deformation belong in the range of the claims in the present invention and equivalent technologies thereof, then the present invention is also intended to comprise these changes.

Claims (6)

1. a multi-model Adaptive Control system, for the nonlinear discrete time system of a class Bounded Linear, it is characterised in that include two Indirect adaptive control device and switching mechanism, described switching mechanism connects described Indirect adaptive control device and the input of a controlled device, institute respectively State Indirect adaptive control device and connect the outfan of described controlled device；The outfan of described controlled device and said two Indirect adaptive control device it Between be provided with a close loop negative feedback, and be set to subtract each other relation between the model output of described controlled device and said two Indirect adaptive control device； The input of described controlled device is selected to produce by described switching mechanism between said two Indirect adaptive control device；Said two indirect self-adaptive control Device processed includes linear robust adaptive controller and nonlinear neural network adaptive controller respectively；

Described linear robust adaptive controller includes linear robust adaptive model and linear robust controller；Described linear robust adaptive model leads to Cross projection identification algorithm, it is ensured that when the restrictive condition of the nonlinear terms of described multi-model Adaptive Control system is loosened to Bounded Linear, described line The Identification Errors also bounded of property robust adaptive model；Described linear robust controller is linear pole-placement and adaptive control device, by described linear pole Point configuration adaptive controller is by the Assignment of Closed-Loop Poles of described multi-model Adaptive Control system to desired locations, thus obtains process non-minimum phase The ability of the control problem of system and open-loop unstable system；Particularly as follows:

Set up system linearity robust adaptive model M₁:

${\widehat{\mathrm{\&zeta;}}}_1\left(k\right)={\mathrm{\&theta;}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)---\left(5\right)$

θ in formula₁(k)=[b_1,0(k),…,b_1,m(k),a_1,0(k),…,a_1,n-1(k)]^T, it is model M₁Parameter in the k moment；

Obtain a N₀> 0 so that all θ ∈ Ω are hadModel M₁Parameter use following projection identification algorithm carry out Update, whereinIt is θ₁The identification of (t):

${\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)={\widehat{\mathrm{\&theta;}}}_1(k-1)+-{\mathrm{\&Gamma;}}_1{\mathrm{\&epsiv;}}_1\mathrm{\&phi;}\left(k\right),{\mathrm{\&theta;}}_1\left(0\right)\&Element;\mathrm{\&Omega;}---\left(6\right)$

${\widehat{\mathrm{\&theta;}}}_1\left(k\right)=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& \begin{array}{cc}if& \left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|\&le;N_0\end{array}\\ \frac{N_0}{\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& otherwise\end{array}\right.---\left(7\right)$

${\mathrm{\&epsiv;}}_1\left(k\right)=\frac{\mathrm{\&zeta;}\left(k\right)-{\widehat{\mathrm{\&theta;}}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)}{m_s^2\left(k\right)}---\left(8\right)$

$m_s^2\left(k\right)={(\mathrm{\&tau;}+|\left|\mathrm{\&phi;}\right(k\left)\right|\left|\right)}^2+n_d\left(k\right)---\left(9\right)$

n_d(k+1)=δ₀n_d(k)+|u_p(k)|²+|y_p(k)|² (10)

In formula,n_d(0)=0,0 < Γ₁<2,ε₁It it is standardized model error；

Make θ₁=[θ_1a,θ_1b],θ_1a=[a_1,n-1,a_1,n-2,…,a_1,0]^T,θ_1b=[b_1,m,b_1,m-1,…,b_1,0]^T,

Linear pole-placement and adaptive control device C is designed according to linear robust adaptive model₁:

Determined by following formulaWith

In formulaA^*Z () is the closed loop proper polynomial of Hurwitz；

In formula, ζ (k) represents the measured value of system output, and φ (k) represents the regression vector of the composition of system input and output, and it is non-that η (k) represents system The measured value of linear term；

For output estimated value,

N₀It it is the upper bound of parameter mould in unknown parameter collection Ω；

Being normalizing parameter, β and γ is the parameter of nonlinear function Bounded Linear condition, its value meet it is assumed that n_d(0)=0,0 < Γ₁<2,ε₁It is standardized model error, m_sK () is normalized signal, n_dK () is dynamic normalized signal.

Multi-model Adaptive Control system the most according to claim 1, it is characterised in that described nonlinear neural network adaptive controller Including nonlinear neural network adaptive model and nonlinear neural network controller, and described nonlinear neural network adaptive model is by linear segment Being grouped into non-linear, the coefficient of described linear segment is updated as auto-adaptive parameter, and described non-linear partial is made up of neutral net；Institute State the nonlinear neural network adaptive model weights by on-line tuning neutral net, thus obtain the estimation to described controlled device and export.

Multi-model Adaptive Control system the most according to claim 2, it is characterised in that described nonlinear neural network controller be with The pole-placement and adaptive control device of nonlinear terms, improves described multi-model by the described pole-placement and adaptive control device with nonlinear terms adaptive Answer the control accuracy of control system.

Multi-model Adaptive Control system the most according to claim 1, it is characterised in that described switching mechanism is provided with performance indications module, And described performance indications module includes that cumulative error part and model error part, described cumulative error part are used for preventing described multi-model self-adapting control The frequent switching of system processed；Described switching mechanism by calculating the performance indications of each controller in each control moment, thus selects performance indications relatively Little controller produces the control input of subsequent time.

5. a multi-model Adaptive Control method, utilizes multi-model Adaptive Control device as claimed in claim 1 to realize the control to controlled device System, it is characterised in that comprise the steps:

S1: system initialization: random initializtion linear robust adaptive model and the parameter of nonlinear neural network adaptive model, and the most initial Change the weights of neutral net；

In the S2:k=0 moment, controlled device is output as 0；When k ≠ 0 moment, controlled device is output as the real output value of system, with system Setting value make difference and obtain the control error e of system_c, the real output value of system obtains model error with the output work difference of linear robust adaptive model e₁, the real output value of system and nonlinear neural network adaptive model are made difference and are obtained model error e₂；

Wherein, described linear robust adaptive model is by projection identification algorithm, it is ensured that when the restriction of the nonlinear terms of multi-model Adaptive Control system When condition is loosened to Bounded Linear, the Identification Errors also bounded of described linear robust adaptive model；Described linear robust controller is linear limit Configuration adaptive controller, is arrived the Assignment of Closed-Loop Poles of described multi-model Adaptive Control system by described linear pole-placement and adaptive control device Desired locations, thus obtain the ability of the control problem processing non-minimum phase system and open-loop unstable system；Particularly as follows:

Set up system linearity robust adaptive model M₁:

${\widehat{\mathrm{\&zeta;}}}_1\left(k\right)={\mathrm{\&theta;}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)---\left(5\right)$

θ in formula₁(k)=[b_1,0(k),…,b_1,m(k),a_1,0(k),…,a_1,n-1(k)]^T, it is model M₁Parameter in the k moment；

Obtain a N₀> 0 so that all θ ∈ Ω are hadModel M₁Parameter use following projection identification algorithm carry out Update, whereinIt is θ₁The identification of (t):

${\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)={\widehat{\mathrm{\&theta;}}}_1(k-1)+-{\mathrm{\&Gamma;}}_1{\mathrm{\&epsiv;}}_1\mathrm{\&phi;}\left(k\right),{\mathrm{\&theta;}}_1\left(0\right)\&Element;\mathrm{\&Omega;}---\left(6\right)$

${\widehat{\mathrm{\&theta;}}}_1\left(k\right)=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& \begin{array}{cc}if& \left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|\&le;N_0\end{array}\\ \frac{N_0}{\left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)\right|}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_1\left(k\right)& otherwise\end{array}\right.---\left(7\right)$

${\mathrm{\&epsiv;}}_1\left(k\right)=\frac{\mathrm{\&zeta;}\left(k\right)-{\widehat{\mathrm{\&theta;}}}_1^T(k-1)\mathrm{\&phi;}\left(k\right)}{m_s^2\left(k\right)}---\left(8\right)$

$m_s^2\left(k\right)={(\mathrm{\&tau;}+|\left|\mathrm{\&phi;}\right(k\left)\right|\left|\right)}^2+n_d\left(k\right)---\left(9\right)$

n_d(k+1)=δ₀n_d(k)+|u_p(k)|²+|y_p(k)|² (10)

In formula,n_d(0)=0,0 < Γ₁<2,ε₁It it is standardized model error；

Make θ₁=[θ_1a,θ_1b],θ_1a=[a_1,n-1,a_1,n-2,…,a_1,0]^T,θ_1b=[b_1,m,b_1,m-1,…,b_1,0]^T,

According to the linear robust adaptive model linear pole-placement and adaptive control device C1 of design:

Determined by following formulaWith

In formulaA^*Z () is the closed loop proper polynomial of Hurwitz；

S3: be utilized respectively the parameter of the parameter computing controller of two models, error e will be controlled_cAs linear robust controller and non-linear neural net The input of network controller, is produced controlled quentity controlled variable u respectively by two controllers₁And u₂；

S4: calculate linear robust controller and the performance index value of nonlinear neural network controller, and select the controller that performance index value is less to produce Raw input u_i, as the control input u of controlled device with linear robust adaptive model and nonlinear neural network adaptive model；

S5: update linear robust adaptive model and the parameter of nonlinear neural network adaptive model and the weights of neutral net respectively；

S6: forward step S2 to；

In formula, ζ (k) represents the measured value of system output, and φ (k) represents the regression vector of the composition of system input and output, and it is non-that η (k) represents system The measured value of linear term

For output estimated value,

N₀It it is the upper bound of parameter mould in unknown parameter collection Ω；

Being normalizing parameter, β and γ is the parameter of nonlinear function Bounded Linear condition, its value meet it is assumed that n_d(0)=0,0 < Γ₁<2,ε₁It is standardized model error, m_sK () is normalized signal, n_dK () is dynamic normalized signal.

Multi-model Adaptive Control method the most according to claim 5, it is characterised in that described neutral net is set to single hidden layer, and described god It is set to 6-10 through the number of the hidden neuron of network.