CN103676646B - A kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag - Google Patents

Abstract

There is a method for estimating state for the random uncertainty of generation and the network control system of distributed sensor time lag, relate to a kind of uncertainty and sensor hangover state method of estimation of random generation.The invention solves uncertainty and distributed sensor time lag that standing state method of estimation can not process random generation simultaneously, and then affect the problem of state estimation performance, the present invention considers the random uncertainty that occurs and distributed sensor time lag to the impact of state estimation performance simultaneously, utilize Liapunov function to consider the effective information of time lag comprehensively, compared with the method for estimating state of existing non-linear complex dynamic systems, method for estimating state of the present invention can process the random uncertainty occurred simultaneously, distributed sensor time lag and time become bounded time lag, obtain the method for estimating state based on LMI solution, reach the object of anti-nonlinear disturbance, the present invention is applicable to the state estimation of non-linear complex dynamic systems.

Description

A kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag

Technical field

The present invention relates to a kind of uncertainty and sensor hangover state method of estimation of random generation.

Background technology

State estimation is a kind of important studying a question in control system, in the Signal estimation task in the fields such as aircraft formation, Global localization system, Target Tracking System, obtain widespread use.

Current existing method for estimating state can not process uncertainty and the distributed sensor time lag of random generation simultaneously, and then affects state estimation performance.

Summary of the invention

The present invention can not process uncertainty and the distributed sensor time lag of random generation simultaneously in order to solve standing state method of estimation, and then affect the problem of state estimation performance, propose a kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag.

A kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag of the present invention, the concrete steps of the method are:

Step one, foundation have the random nonlinear dynamical model that the network control system of uncertainty and distributed sensor time lag occurs, and its state space form is:

x _k+1＝(A+α _k△A)x _k+Bf(x _k)(1)

$y_k={\mathrm{Cx}}_k+{\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\τ}=1}{\overset{-\mathrm{\∞}}{\Σ}}{\mathrm{\μ}}_{\mathrm{\τ}}{x}_{k-\mathrm{\τ}}---\left(2\right)$

In formula, x _kfor the state variable of the nonlinear dynamical model of the network control system in k moment, x _k+1for the state variable of the nonlinear dynamical model of the network control system in k+1 moment; d _kfor bounded Time-varying time-delays, for k-d _kthe state variable of the nonlinear dynamical model of the network control system in moment, x _k-τfor the state variable of the nonlinear dynamical model of the network control system in k-τ moment; y _kfor the sensor measurement output function in k moment; A, B, C, D, E are system matrix; F (x _k) be nonlinear disturbance function, wherein, f (0)=0, || f (x) ||≤|| Ω x||, || f (x) || be the norm of nonlinear disturbance, Ω is constant matrices; △ A=MFN is norm-bounded parameter uncertainty matrix, and M, F and N are the matrix portraying norm-bounded parameter uncertainty, and matrix F meets F ^tf≤I, I are unit matrix, μ _τfor portraying the constant of distributed sensor time lag, wherein, τ=1,2 ... ,+∞; α _kfor obeying the stochastic variable of Bernoulli Jacob's distribution;

Step 2, state estimation is carried out to the nonlinear dynamical model of the network control system with the random uncertainty that occurs and distributed sensor time lag;

State estimator formula:

${\hat{x}}_{k+1}=A{\hat{x}}_k+Bf\left({\hat{x}}_k\right)+G(y_k-C{\hat{x}}_k)---\left(3\right)$

In formula for x _kin the state estimation in k moment, for the estimation function of nonlinear disturbance, G is state estimation gain matrix;

Step 3, according to step 2 to there is the random state estimation that the nonlinear dynamical model of the network control system of uncertain and distributed sensor time lag occurs, computing mode evaluated error:

Utilize formula (1) to deduct formula (3) and obtain state estimation error equation:

$e_{k+1}=(A-GC)e_k+{\mathrm{\α}}_k{\mathrm{\ΔAx}}_k+Bf\left(e_k\right)-G({\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\τ}=1}{\overset{+\mathrm{\∞}}{\Σ}}{\mathrm{\μ}}_{\mathrm{\τ}}{x}_{k-\mathrm{\τ}})---\left(4\right)$

In formula, for the state estimation error in k moment, e _k+1for the state estimation error in k+1 moment, $f\left(e_k\right)=f\left(x_k\right)-f\left({\hat{x}}_k\right);$

Step 4, the state estimation error obtained according to step 3, obtain state estimation augmented system;

${\mathrm{\η}}_{k+1}=(\stackrel{\‾}{A}+\stackrel{\‾}{\mathrm{\α}}\mathrm{\Δ}\stackrel{\‾}{A}){\mathrm{\η}}_k+({\mathrm{\α}}_k-\stackrel{\‾}{\mathrm{\α}})\mathrm{\Δ}\stackrel{\‾}{A}{\mathrm{\η}}_k+\stackrel{\‾}{B}f\left({\mathrm{\η}}_k\right)+\stackrel{\‾}{D}{\mathrm{\η}}_{k-d_k}+\stackrel{\‾}{E}\underset{\mathrm{\τ}=1}{\overset{+\mathrm{\∞}}{\Σ}}{\mathrm{\μ}}_{\mathrm{\τ}}{x}_{k-\mathrm{\τ}}---\left(5\right)$

In formula (5), ${\mathrm{\η}}_k={\left[\begin{array}{cc}{x}_k^T& e_k^T\end{array}\right]}^T,{\mathrm{\η}}_{k-d_k}={\left[\begin{array}{cc}{x}_{k-d_k}^T& e_{k-d_k}^T\end{array}\right]}^T,$ for state variable x _ktransposition, for stochastic variable α _kaverage, the form of formula (5) matrix is:

$\stackrel{\‾}{A}=\left[\begin{array}{cc}A& 0\\ 0& A-GC\end{array}\right],$ $\mathrm{\Δ}\stackrel{\‾}{A}=\left[\begin{array}{cc}\mathrm{\Δ}A& 0\\ \mathrm{\Δ}A& 0\end{array}\right],$ $\stackrel{\‾}{B}=\left[\begin{array}{cc}B& 0\\ 0& B\end{array}\right],$

$\stackrel{\‾}{D}=\left[\begin{array}{cc}0& 0\\ -GD& 0\end{array}\right],$ $\stackrel{\‾}{E}=\left[\begin{array}{cc}0& 0\\ -GE& 0\end{array}\right],$ $f\left({\mathrm{\η}}_k\right)=\left[\begin{array}{c}f\left(x_k\right)\\ f\left(e_k\right)\end{array}\right];$

Step 5, utilization state estimate augmented system, by liapunov's theorem of stability, obtain state estimation gain matrix G: by formula:

$\left[\begin{array}{ccccc}{\mathrm{\&Xi;}}_{11}+\mathrm{\&epsiv;}{\tilde{N}}^T\tilde{N}& 0& 0& {\mathrm{\&Xi;}}_{14}& 0\\ 0& -\stackrel{\&OverBar;}{Q}& 0& {\mathrm{\&Xi;}}_{24}& 0\\ 0& 0& -\frac{1}{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}\stackrel{\&OverBar;}{R}& {\mathrm{\&Xi;}}_{34}& 0\\ {\mathrm{\&Xi;}}_{14}^T& {\mathrm{\&Xi;}}_{24}^T& {\mathrm{\&Xi;}}_{34}^T& {\mathrm{\&Xi;}}_{44}& {\mathrm{\&Xi;}}_{45}\\ 0& 0& 0& {\mathrm{\&Xi;}}_{45}^T& -\mathrm{\&epsiv;}I\end{array}\right]<0,---\left(6\right)$

${\stackrel{\&OverBar;}{B}}^T\stackrel{\&OverBar;}{PB}\&le;{\mathrm{\&lambda;}}^{*}I,---\left(7\right)$

Obtain matrix P ₂and X, pass through formula

$G=P_2^{-1}X---\left(8\right)$

Computing mode estimated gain matrix G; Formula (6) and the middle matrix concrete form of formula (7):

${\mathrm{\&Xi;}}_{11}=(d_M-d_m+1)\stackrel{\&OverBar;}{Q}+4{\mathrm{\&lambda;}}^{*}{\stackrel{\&OverBar;}{F}}^T\stackrel{\&OverBar;}{F}+\stackrel{\&OverBar;}{\mathrm{\&mu;}}\stackrel{\&OverBar;}{R}-\stackrel{\&OverBar;}{P}$

Ξ ₁₄＝[Ξ ₁₄₁Ξ ₁₄₂000]

Ξ ₂₄＝[Ξ ₂₄₁00Ξ ₂₄₄0]

Ξ ₃₄＝[Ξ ₃₄₁000Ξ ₃₄₅]

Ξ ₁₄₁＝Ξ ₁₄₂＝diag{A ^TP ₁,A ^TP ₂-C ^TX ^T}

${\mathrm{\&Xi;}}_{241}={\mathrm{\&Xi;}}_{244}=\left[\begin{array}{cc}0& -D^T{X}^T\\ 0& 0\end{array}\right],$

${\mathrm{\&Xi;}}_{341}={\mathrm{\&Xi;}}_{345}=\left[\begin{array}{cc}0& -E^T{X}^T\\ 0& 0\end{array}\right]$

${\mathrm{\&Xi;}}_{44}=diag\{-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P}\}$

${\mathrm{\&Xi;}}_{45}^T=\&lsqb;\begin{array}{ccccc}\stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \sqrt{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}(1-\stackrel{\&OverBar;}{\mathrm{\&alpha;}})}{M}^T{\tilde{P}}^T& 0& 0\end{array}\&rsqb;$

$\tilde{P}=\left[\begin{array}{c}{P}_1\\ P_2\end{array}\right],$

$\tilde{N}=\&lsqb;\begin{array}{cc}N& 0\end{array}\&rsqb;,$

$\stackrel{\&OverBar;}{F}=diag\{\mathrm{\&Omega;},\mathrm{\&Omega;}\}$

$\stackrel{\&OverBar;}{P}=diag\{P_1,P_2\}$

Diag{} represents diagonal matrix, the convergence coefficient of Distributed delay d _mfor Time-varying time-delays d _kupper bound information _,d _mfor Time-varying time-delays d _klower bound information, X is matrix, λ ^*normal number is, E with ε ^tfor the transposition of matrix E, E ^tx ^tfor matrix E ^twith matrix X ^tproduct; with be symmetric positive definite matrix, P ₁and P ₂be symmetric positive definite matrix;

Step 6, bring the state estimation gain matrix G that step 5 obtains into state estimator formula in step 2, realize the state estimation to the network control system with the random uncertainty that occurs and distributed sensor time lag.

Method for estimating state of the present invention considers the random uncertainty that occurs and distributed sensor time lag to the impact of state estimation performance simultaneously, utilize Liapunov function to consider the effective information of time lag comprehensively, compared with the method for estimating state of existing non-linear complex dynamic systems, method for estimating state of the present invention can process the random uncertainty occurred simultaneously, distributed sensor time lag and time become bounded time lag, obtain the method for estimating state based on LMI solution, reach the object of anti-nonlinear disturbance, and have and be easy to solve and the advantage realized.

Accompanying drawing explanation

Fig. 1 is the method for the invention process flow diagram;

Fig. 2 is virtual condition track x _{k, 1}and state estimation track comparison diagram, in figure, solid line is virtual condition track x _{k, 1}, dotted line is state estimation track

Fig. 3 is virtual condition track x _{k, 2}and state estimation track comparison diagram, in figure, solid line is virtual condition track x _{k, 2}, dotted line is state estimation track

Fig. 4 is virtual condition track x _{k, 3}and state estimation track comparison diagram, in figure, solid line is virtual condition track x _{k, 3}, dotted line is state estimation track

Fig. 5 is state estimation error locus e _{k, 1}, e _{k, 2}, e _{k, 3}comparison diagram, in figure, solid line is state estimation error locus e _{k, 1}, the line of round dot and dotted line composition is state estimation error locus e _{k, 2}, dotted line is state estimation error locus e _{k, 3}.

Embodiment

Embodiment one, composition graphs one illustrate present embodiment, a kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag described in present embodiment, and the concrete steps of the method are:

Step one, foundation have the random nonlinear dynamical model that the network control system of uncertainty and distributed sensor time lag occurs, and its state space form is:

x _k+1＝(A+α _k△A)x _k+Bf(x _k)(1)

$y_k={\mathrm{Cx}}_k+{\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}}---\left(2\right)$

In formula, x _kfor the state variable of the nonlinear dynamical model of the network control system in k moment, x _k+1for the state variable of the nonlinear dynamical model of the network control system in k+1 moment; d _kfor bounded Time-varying time-delays, for k-d _kthe state variable of the nonlinear dynamical model of the network control system in moment, x _k-τfor the state variable of the nonlinear dynamical model of the network control system in k-τ moment; y _kfor the sensor measurement output function in k moment; A, B, C, D, E are system matrix; F (x _k) be nonlinear disturbance function, wherein, f (0)=0, || f (x) ||≤|| Ω x||, || f (x) || be the norm of nonlinear disturbance, Ω is constant matrices; △ A=MFN is norm-bounded parameter uncertainty matrix, and M, F and N are the matrix portraying norm-bounded parameter uncertainty, and matrix F meets F ^tf≤I, I are unit matrix, μ _τfor portraying the constant of distributed sensor time lag, wherein, τ=1,2 ... ,+∞; α _kfor obeying the stochastic variable of Bernoulli Jacob's distribution;

Step 2, state estimation is carried out to the nonlinear dynamical model of the network control system with the random uncertainty that occurs and distributed sensor time lag;

State estimator formula:

${\hat{x}}_{k+1}=A{\hat{x}}_k+Bf\left({\hat{x}}_k\right)+G(y_k-C{\hat{x}}_k)---\left(3\right)$

In formula for x _kin the state estimation in k moment, for the estimation function of nonlinear disturbance, G is state estimation gain matrix;

Step 3, according to step 2 to there is the random state estimation that the nonlinear dynamical model of the network control system of uncertain and distributed sensor time lag occurs, computing mode evaluated error:

Utilize formula (1) to deduct formula (3) and obtain state estimation error equation:

$e_{k+1}=(A-GC)e_k+{\mathrm{\&alpha;}}_k{\mathrm{\&Delta;Ax}}_k+Bf\left(e_k\right)-G({\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}})---\left(4\right)$

In formula, for the state estimation error in k moment, e _k+1for the state estimation error in k+1 moment, $f\left(e_k\right)=f\left(x_k\right)-f\left({\hat{x}}_k\right);$

Step 4, the state estimation error obtained according to step 3, obtain state estimation augmented system;

${\mathrm{\&eta;}}_{k+1}=(\stackrel{\&OverBar;}{A}+\stackrel{\&OverBar;}{\mathrm{\&alpha;}}\stackrel{\&OverBar;}{\mathrm{\&Delta;}}\stackrel{\&OverBar;}{A}){\mathrm{\&eta;}}_k+({\mathrm{\&alpha;}}_k-\stackrel{\&OverBar;}{\mathrm{\&alpha;}})\mathrm{\&Delta;}\stackrel{\&OverBar;}{A}{\mathrm{\&eta;}}_k+\stackrel{\&OverBar;}{B}f\left({\mathrm{\&eta;}}_k\right)+\stackrel{\&OverBar;}{D}{\mathrm{\&eta;}}_{k-d_k}+\stackrel{\&OverBar;}{E}\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}}---\left(5\right)$

In formula (5), ${\mathrm{\&eta;}}_k={\left[\begin{array}{cc}{x}_k^T& e_k^T\end{array}\right]}^T,{\mathrm{\&eta;}}_{k-d_k}={\left[\begin{array}{cc}{x}_{k-d_k}^T& e_{k-d_k}^T\end{array}\right]}^T,$ for state variable x _ktransposition, for stochastic variable α _kaverage, the form of formula (5) matrix is:

$\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}A& 0\\ 0& A-GC\end{array}\right],$ $\mathrm{\&Delta;}\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}\mathrm{\&Delta;}A& 0\\ \mathrm{\&Delta;}A& 0\end{array}\right],$ $\stackrel{\&OverBar;}{B}=\left[\begin{array}{cc}B& 0\\ 0& B\end{array}\right],$

$\stackrel{\&OverBar;}{D}=\left[\begin{array}{cc}0& 0\\ -GD& 0\end{array}\right],$ $\stackrel{\&OverBar;}{E}=\left[\begin{array}{cc}0& 0\\ -GE& 0\end{array}\right],$ $f\left({\mathrm{\&eta;}}_k\right)=\left[\begin{array}{c}f\left(x_k\right)\\ f\left(e_k\right)\end{array}\right];$

Step 5, utilization state estimate augmented system, by liapunov's theorem of stability, obtain state estimation gain matrix G;

By formula:

$\left[\begin{array}{ccccc}{\mathrm{\&Xi;}}_{11}+\mathrm{\&epsiv;}{\tilde{N}}^T\tilde{N}& 0& 0& {\mathrm{\&Xi;}}_{14}& 0\\ 0& -\stackrel{\&OverBar;}{Q}& 0& {\mathrm{\&Xi;}}_{24}& 0\\ 0& 0& -\frac{1}{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}\stackrel{\&OverBar;}{R}& {\mathrm{\&Xi;}}_{34}& 0\\ {\mathrm{\&Xi;}}_{14}^T& {\mathrm{\&Xi;}}_{24}^T& {\mathrm{\&Xi;}}_{34}^T& {\mathrm{\&Xi;}}_{44}& {\mathrm{\&Xi;}}_{45}\\ 0& 0& 0& {\mathrm{\&Xi;}}_{45}^T& -\mathrm{\&epsiv;}I\end{array}\right]<0,---\left(6\right)$

${\stackrel{\&OverBar;}{B}}^T\stackrel{\&OverBar;}{PB}\&le;{\mathrm{\&lambda;}}^{*}I,---\left(7\right)$

Obtain matrix P ₂and X, pass through formula

$G=P_2^{-1}X---\left(8\right)$

Computing mode estimated gain matrix G; Formula (6) and the middle matrix concrete form of formula (7):

${\mathrm{\&Xi;}}_{11}=(d_M-d_m+1)\stackrel{\&OverBar;}{Q}+4{\mathrm{\&lambda;}}^{*}{\stackrel{\&OverBar;}{F}}^T\stackrel{\&OverBar;}{F}+\stackrel{\&OverBar;}{\mathrm{\&mu;}}\stackrel{\&OverBar;}{R}-\stackrel{\&OverBar;}{P}$

Ξ ₁₄＝[Ξ ₁₄₁Ξ ₁₄₂000]

Ξ ₂₄＝[Ξ ₂₄₁00Ξ ₂₄₄0]

Ξ ₃₄＝[Ξ ₃₄₁000Ξ ₃₄₅]

Ξ ₁₄₁＝Ξ ₁₄₂＝diag{A ^TP ₁,A ^TP ₂-C ^TX ^T}

${\mathrm{\&Xi;}}_{241}={\mathrm{\&Xi;}}_{244}=\left[\begin{array}{cc}0& -D^T{X}^T\\ 0& 0\end{array}\right],$

${\mathrm{\&Xi;}}_{341}={\mathrm{\&Xi;}}_{345}=\left[\begin{array}{cc}0& -E^T{X}^T\\ 0& 0\end{array}\right],$

${\mathrm{\&Xi;}}_{44}=diag\{-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P}\}$

${\mathrm{\&Xi;}}_{45}^T=\&lsqb;\begin{array}{ccccc}\stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \sqrt{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}(1-\stackrel{\&OverBar;}{\mathrm{\&alpha;}})}{M}^T{\tilde{P}}^T& 0& 0\end{array}\&rsqb;$

$\tilde{P}=\left[\begin{array}{c}{P}_1\\ P_2\end{array}\right],$

$\tilde{N}=\left[\begin{array}{cc}N& 0\end{array}\right],$

$\stackrel{\&OverBar;}{F}=diag\{\mathrm{\&Omega;},\mathrm{\&Omega;}\}$

$\stackrel{\&OverBar;}{P}=diag\{P_1,P_2\}$

Diag{} represents diagonal matrix, the convergence coefficient of Distributed delay d _mfor Time-varying time-delays d _kupper bound information, d _mfor Time-varying time-delays d _klower bound information, X is matrix, λ ^*normal number is, E with ε ^tfor the transposition of matrix E, E ^tx ^tfor matrix E ^twith matrix X ^tproduct; with be symmetric positive definite matrix, P ₁and P ₂be symmetric positive definite matrix,

Step 6, bringing the state estimation gain matrix G that step 5 obtains into state estimator formula in step 2, realizing having the random state estimation that the network control system of uncertain and distributed sensor time lag occurs.

Embodiment two, present embodiment have further illustrating of the method for estimating state of the network control system of the random uncertainty that occurs and distributed sensor time lag to a kind of described in embodiment one, and the lyapunov stability theory described in step 5 is:

V(η _k+1)-V(η _k)<0

Wherein:

V(η _k)＝V ₁(η _k)+V ₂(η _k)+V ₃(η _k)(9)

$V_1\left({\mathrm{\&eta;}}_k\right)={\mathrm{\&eta;}}_k^T\stackrel{\&OverBar;}{P}{\mathrm{\&eta;}}_k,V_2\left({\mathrm{\&eta;}}_k\right)=\underset{l=k-d_k}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{Q}{\mathrm{\&eta;}}_l+\underset{j=-d_M+1}{\overset{-d_m}{\&Sigma;}}\underset{l=k+j}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{Q}{\mathrm{\&eta;}}_l,V_3\left({\mathrm{\&eta;}}_k\right)=\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}\underset{l=k-\mathrm{\&tau;}}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{R}{\mathrm{\&eta;}}_l)$

In formula, V (η _k) be the Liapunov function in k moment, V (η _k+1) be the Liapunov function in k+1 moment, ${\mathrm{\&eta;}}_l={\left[\begin{array}{cc}{x}_l^T& e_l^T\end{array}\right]}^T$ For the variable in l moment, for η _ktransposition, for η _ltransposition.

The method of the invention is adopted to emulate:

Systematic parameter:

$A=\left[\begin{array}{ccc}-0.3& 0.01& 0\\ 0& 0.26& -0.01\\ -0.06& 0& 0.4\end{array}\right],$ $B=\left[\begin{array}{ccc}-0.1& 0.2& 0.1\\ 0.2& 0.1& -0.03\\ -0.1& -0.2& 0.3\end{array}\right]$

$C=\left[\begin{array}{ccc}0& -0.1& 0.1\\ 0.1& 0.2& 0.3\end{array}\right],$ $D=\left[\begin{array}{ccc}0.1& -0.2& 0.2\\ 0.2& -0.15& 0.1\end{array}\right],$ $E=\left[\begin{array}{ccc}0.4& 0.1& -0.1\\ 0& -0.1& 0.25\end{array}\right]$

M＝[0.41.20.7] ^T,N＝[-0.20.10],F＝sin(0.45k)

In addition, d _m=3, d _m=5, μ _p=2 ^-3-p, f (x _k)=[-0.1x _{k, 1}tanh (0.1x _{k, 2}) 0.2x _{k, 3}] ^t, Σ=diag{0.1,0.1,0.2}.

State estimation gain solves:

Formula (6), formula (7) and formula (8) solve, and obtaining state estimator gain matrix G is following form

$G=\left[\begin{array}{cc}0.0714& -0.1349\\ -0.2833& 0.3909\\ -0.1346& 0.4613\end{array}\right]$

State estimator effect:

Fig. 2 is virtual condition track x _{k, 1}and state estimation track fig. 3 is virtual condition track x _{k, 2}and state estimation track fig. 4 is virtual condition track x _{k, 3}and state estimation track fig. 5 is state estimation error locus e _k,i(i=1,2,3).

From Fig. 2 to Fig. 5, for having the random uncertainty of generation and the network control system of distributed sensor time lag, the state estimator design method of inventing can estimate dbjective state effectively.

Claims (2)

1. have a method for estimating state for the random uncertainty of generation and the network control system of distributed sensor time lag, it is characterized in that, the concrete steps of the method are:

Step one, foundation have the nonlinear dynamical model of the random uncertainty of generation and the network control system of distributed sensor time lag, and its state space form is:

x _k+1＝(A+α _k△A)x _k+Bf(x _k)(1)

$y_k={\mathrm{Cx}}_k+{\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}}---\left(2\right)$

In formula, x _kfor the state variable of the nonlinear dynamical model of the network control system in k moment, x _k+1for the state variable of the nonlinear dynamical model of the network control system in k+1 moment; d _kfor bounded Time-varying time-delays, for k-d _kthe state variable of the nonlinear dynamical model of the network control system in moment, x _k-τfor the state variable of the nonlinear dynamical model of the network control system in k-τ moment; y _kfor the sensor measurement output function in k moment; A, B, C, D, E are system matrix; F (x _k) be nonlinear disturbance function, wherein, f (0)=0, || f (x) ||≤|| Ω x||, || f (x) || be the norm of nonlinear disturbance, Ω is constant matrices; △ A=MFN is norm-bounded parameter uncertainty matrix, and M, F and N are the matrix portraying norm-bounded parameter uncertainty, and matrix F meets F ^tf≤I, I are unit matrix, μ _τfor portraying the constant of distributed sensor time lag, wherein, τ=1,2 ... ,+∞; α _kfor obeying the stochastic variable of Bernoulli Jacob's distribution;

Step 2, state estimation is carried out to the nonlinear dynamical model of the network control system with the random uncertainty that occurs and distributed sensor time lag;

State estimator formula:

${\hat{x}}_{k+1}=A{\hat{x}}_k+Bf\left({\hat{x}}_k\right)+G(y_k-C{\hat{x}}_k)---\left(3\right)$

In formula for x _kin the state estimation in k moment, for the estimation function of nonlinear disturbance, G is state estimation gain matrix;

Step 3, according to step 2 to there is the random state estimation that the nonlinear dynamical model of the network control system of uncertain and distributed sensor time lag occurs, computing mode evaluated error:

Utilize formula (1) to deduct formula (3) and obtain state estimation error equation:

$e_{k+1}=(A-GC)e_k+{\mathrm{\&alpha;}}_k{\mathrm{\&Delta;Ax}}_k+Bf\left(e_k\right)-G({\mathrm{Dx}}_{k-d_k}+E\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}})---\left(4\right)$

In formula, for the state estimation error in k moment, e _k+1for the state estimation error in k+1 moment,

$f\left(e_k\right)=f\left(x_k\right)-f\left({\hat{x}}_k\right);$

Step 4, the state estimation error obtained according to step 3, obtain state estimation augmented system;

${\mathrm{\&eta;}}_{k+1}=(\stackrel{\&OverBar;}{A}+\stackrel{\&OverBar;}{\mathrm{\&alpha;}}\mathrm{\&Delta;}\stackrel{\&OverBar;}{A}){\mathrm{\&eta;}}_k+({\mathrm{\&alpha;}}_k-\stackrel{\&OverBar;}{\mathrm{\&alpha;}})\mathrm{\&Delta;}\stackrel{\&OverBar;}{A}{\mathrm{\&eta;}}_k+\stackrel{\&OverBar;}{B}f\left({\mathrm{\&eta;}}_k\right)+\stackrel{\&OverBar;}{D}{\mathrm{\&eta;}}_{k-d_k}+\stackrel{\&OverBar;}{E}\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}{x}_{k-\mathrm{\&tau;}}---\left(5\right)$

In formula (5) ${\mathrm{\&eta;}}_k={\left[\begin{array}{cc}{x}_k^T& e_k^T\end{array}\right]}^T,$ ${\mathrm{\&eta;}}_{k-d_k}={\left[\begin{array}{cc}{x}_{k-d_k}^T& e_{k-d_k}^T\end{array}\right]}^T,$ for state variable x _ktransposition, for stochastic variable α _kaverage, the form of formula (5) matrix is:

$\begin{array}{ccc}\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}A& 0\\ 0& A-GC\end{array}\right],& \mathrm{\&Delta;}\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}\mathrm{\&Delta;}A& 0\\ \mathrm{\&Delta;}A& 0\end{array}\right],& \stackrel{\&OverBar;}{B}=\left[\begin{array}{cc}B& 0\\ 0& B\end{array}\right]\end{array},$

$\begin{array}{ccc}\stackrel{\&OverBar;}{D}=\left[\begin{array}{cc}0& 0\\ -GD& 0\end{array}\right],& \stackrel{\&OverBar;}{E}=\left[\begin{array}{cc}0& 0\\ -GE& 0\end{array}\right],& f\left({\mathrm{\&eta;}}_k\right)=\left[\begin{array}{c}f\left(x_k\right)\\ f\left(e_k\right)\end{array}\right]\end{array};$

Step 5, utilization state estimate augmented system, by liapunov's theorem of stability, obtain state estimation gain matrix G;

By formula:

$\left[\begin{array}{ccccc}{\mathrm{\&Xi;}}_{11}+\mathrm{\&epsiv;}{\tilde{N}}^T\tilde{N}& 0& 0& {\mathrm{\&Xi;}}_{14}& 0\\ 0& -\stackrel{\&OverBar;}{Q}& 0& {\mathrm{\&Xi;}}_{24}& 0\\ 0& 0& -\frac{1}{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}\stackrel{\&OverBar;}{R}& {\mathrm{\&Xi;}}_{34}& 0\\ {\mathrm{\&Xi;}}_{14}^T& {\mathrm{\&Xi;}}_{24}^T& {\mathrm{\&Xi;}}_{34}^T& {\mathrm{\&Xi;}}_{44}& {\mathrm{\&Xi;}}_{45}\\ 0& 0& 0& {\mathrm{\&Xi;}}_{45}^T& -\mathrm{\&epsiv;}I\end{array}\right]<0,---\left(6\right)$

${\stackrel{\&OverBar;}{B}}^T\stackrel{\&OverBar;}{PB}\&le;{\mathrm{\&lambda;}}^{*}I,---\left(7\right)$

Obtain matrix P ₂and X, pass through formula

$G=PX_2^{-1}---\left(8\right)$

Computing mode estimated gain matrix G; Formula (6) and the middle matrix concrete form of formula (7):

${\mathrm{\&Xi;}}_{11}=(d_M-d_m+1)\stackrel{\&OverBar;}{Q}+4{\mathrm{\&lambda;}}^{*}{\stackrel{\&OverBar;}{F}}^T\stackrel{\&OverBar;}{F}+\stackrel{\&OverBar;}{\mathrm{\&mu;}}\stackrel{\&OverBar;}{R}-\stackrel{\&OverBar;}{P}$

Ξ ₁₄＝[Ξ ₁₄₁Ξ ₁₄₂000]

Ξ ₂₄＝[Ξ ₂₄₁00Ξ ₂₄₄0]

Ξ ₃₄＝[Ξ ₃₄₁000Ξ ₃₄₅]

Ξ ₁₄₁＝Ξ ₁₄₂＝diag{A ^TP ₁,A ^TP ₂-C ^TX ^T}

${\mathrm{\&Xi;}}_{241}={\mathrm{\&Xi;}}_{244}=\left[\begin{array}{cc}0& -D^T{X}^T\\ 0& 0\end{array}\right],$

${\mathrm{\&Xi;}}_{341}={\mathrm{\&Xi;}}_{345}=\left[\begin{array}{cc}0& -E^T{X}^T\\ 0& 0\end{array}\right]$

${\mathrm{\&Xi;}}_{44}=diag\{-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P},-\stackrel{\&OverBar;}{P}\}$

${\mathrm{\&Xi;}}_{45}^T=\left[\begin{array}{ccccc}\stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \stackrel{\&OverBar;}{\mathrm{\&alpha;}}{M}^T{\tilde{P}}^T& \sqrt{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}(1-\stackrel{\&OverBar;}{\mathrm{\&alpha;}})}{M}^T{\tilde{P}}^T& 0& 0\end{array}\right]$

$\tilde{P}=\left[\begin{array}{c}{P}_1\\ P_2\end{array}\right],$

$\tilde{N}=\left[\begin{array}{cc}N& 0\end{array}\right],$

$\stackrel{\&OverBar;}{F}=diag\{\mathrm{\&Omega;},\mathrm{\&Omega;}\}$

$\stackrel{\&OverBar;}{P}=diag\{P_1,P_2\}$

Diag{} represents diagonal matrix, the convergence coefficient of Distributed delay d _mfor Time-varying time-delays d _kupper bound information, d _mfor Time-varying time-delays d _klower bound information, X is matrix, λ ^*normal number is, E with ε ^tfor the transposition of matrix E, E ^tx ^tfor matrix E ^twith matrix X ^tproduct; , with be symmetric positive definite matrix, P ₁and P ₂be symmetric positive definite matrix,

Step 6, bringing the state estimation gain matrix G that step 5 obtains into state estimator formula in step 2, realizing having the random state estimation that the network control system of uncertain and distributed sensor time lag occurs.

2. a kind of method for estimating state with the random uncertainty of generation and the network control system of distributed sensor time lag according to claim 1, it is characterized in that, the lyapunov stability theory described in step 5 is:

V(η _k+1)-V(η _k)<0

Wherein:

V(η _k)＝V ₁(η _k)+V ₂(η _k)+V ₃(η _k)(9)

$V_1\left({\mathrm{\&eta;}}_k\right)={\mathrm{\&eta;}}_k^T\stackrel{\&OverBar;}{P}{\mathrm{\&eta;}}_k,V_2\left({\mathrm{\&eta;}}_k\right)=\underset{l=k-d_k}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{Q}{\mathrm{\&eta;}}_1+\underset{j=-d_M+1}{\overset{-d_m}{\&Sigma;}}\underset{l=k+j}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{Q}{\mathrm{\&eta;}}_l,V_3\left({\mathrm{\&eta;}}_k\right)=\underset{\mathrm{\&tau;}=1}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{\&tau;}}\underset{l=k-\mathrm{\&tau;}}{\overset{k-1}{\&Sigma;}}{\mathrm{\&eta;}}_l^T\stackrel{\&OverBar;}{R}{\mathrm{\&eta;}}_l$

In formula, V (η _k) be the Liapunov function in k moment, V (η _k+1) be the Liapunov function in k+1 moment, ${\mathrm{\&eta;}}_l={\left[\begin{array}{cc}{x}_l^T& e_l^T\end{array}\right]}^T$ For the variable in l moment, for η _ktransposition, for η _ltransposition.