非齐次马尔可夫LPV系统的H∞异步控制

doi:10.3969/j.issn.1001-506X.2020.05.24

Abstract

Abstract:

This paper investigates the problem of asynchronous H_∞ control of a class of discrete-time non-homogeneous Markov jump linear parameter-varying (LPV) systems with external disturbances. Considering that actual system modes of non-homogeneous Markov system are difficult to acquire directly, a non-homogeneous hidden Markov model is adopted to describe the asynchronous phenomenon between controller modes and system modes. The time-varying properties of non-homogeneous Markov jump systems and non-homogeneous hidden Markov chains are described by piecewise homogeneous transition probability matrices and piecewise homogeneous conditional probability matrices, respectively, and they are governed by the same higher-level homogeneous Markov chain. Based on the above-mentioned issues, this paper accomplishes the stability analysis, H_∞ performance analysis and asynchronous H_∞ controller design of the closed-loop system with external disturbance input and asynchronous phenomenon to guarantee the system with the achieved H_∞ performance index. Finally, a practical example of a direct current motor is provided to illustrate the validity and superiority of the developed theoretical results allowing for non-homogeneous information.

Key words: non-homogeneous Markov jump system (MJS), non-homogeneous hidden Markov chain, time-varying transition probability, piecewise homogeneous transition probability, asynchronous H_∞ control

CLC Number:

TP273

Weiyang SUN, Yu LIU. Asynchronous H_∞ control for a class of non-homogeneous Markov jump LPV systems[J]. Systems Engineering and Electronics, 2020, 42(5): 1152-1159.

Figures/Tables 5

Table 1

Table 2

Table 3

Table 4

Fig.1

References 26

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系统模态	a_{i, 11}	a_{i, 12}	a_{i, 21}	a_{i, 22}	a_{i, 31}	a_{i, 33}	b_{i, 1}	b_{i, 2}
i=1	-0.479 9	5.154 6	-3.816 3	14.473 2	0.139 9	-0.925 6	5.870 6	15.501 1
i=2	-1.602 6	9.163 2	-0.591 9	3.031 7	0.074 1	0.074 1	10.285 1	2.228 3
i=3	0.634 6	0.917 8	-0.505 7	2.481 2	0.386 6	0.098 2	0.787 5	1.530 3

状态转移概率矩阵	Θ^Ⅰ	Θ^Ⅱ	Θ^Ⅲ	Θ^Ⅳ	Θ^Ⅴ
Θ	$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$	$\left[\begin{array}{cc}0.3 & 0.7 \\ 0.8 & 0.2\end{array}\right]$	$\left[\begin{array}{cc}0.5 & 0.5 \\ 0.5 & 0.5\end{array}\right]$	$\left[\begin{array}{ll}0.7 & 0.3 \\ 0.2 & 0.8\end{array}\right]$	$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

条件转移概率矩阵	{Λ₁^Ⅰ, Λ₂^Ⅰ}	{Λ₁^Ⅱ, Λ₂^Ⅱ}	{Λ₁^Ⅲ, Λ₂^Ⅲ}	{Λ₁^Ⅳ, Λ₂^Ⅳ}	{Λ₁^Ⅴ, Λ₂^Ⅴ}
Λ₁	$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$	$\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0.1 & 0.05 & 0.85\end{array}\right]$	$\left[\begin{array}{ccc}0.85 & 0.1 & 0.05 \\ 0 & 1 & 0 \\ 0.1 & 0.05 & 0.85\end{array}\right]$	$\left[\begin{array}{ccc}0.85 & 0.1 & 0.05 \\ 0.02 & 0.97 & 0.01 \\ 0.1 & 0.05 & 0.85\end{array}\right]$	$\left[\begin{array}{ccc}0.25 & 0.23 & 0.52 \\ 0.21 & 0.28 & 0.51 \\ 0.32 & 0.41 & 0.27\end{array}\right]$
Λ₂	$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$	$\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0.1 & 0.1 & 0.8\end{array}\right]$	$\left[\begin{array}{ccc}0.9 & 0.05 & 0.05 \\ 0 & 1 & 0 \\ 0.1 & 0.1 & 0.8\end{array}\right]$	$\left[\begin{array}{lll}0.9 & 0.05 & 0.05 \\ 0.07 & 0.9 & 0.03 \\ 0.1 & 0.1 & 0.8\end{array}\right]$	$\left[\begin{array}{ccc}0.42 & 0.23 & 0.35 \\ 0.28 & 0.33 & 0.39 \\ 0.39 & 0.4 & 0.21\end{array}\right]$

γ_opt	{Λ₁^Ⅰ, Λ₂^Ⅰ}	{Λ₁^Ⅱ, Λ₂^Ⅱ}	{Λ₁^Ⅲ, Λ₂^Ⅲ}	{Λ₁^Ⅳ, Λ₂^Ⅳ}	{Λ₁^Ⅴ, Λ₂^Ⅴ}
Θ^Ⅰ	0.173	0.177	0.263	0.368	1.214
Θ^Ⅱ	0.186	0.192	0.288	0.403	1.359
Θ^Ⅲ	0.195	0.203	0.308	0.422	1.363
Θ^Ⅳ	0.253	0.265	0.388	0.505	1.428
Θ^Ⅴ	1.438	1.499	2.406	2.942	无解

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Asynchronous H_∞ control for a class of non-homogeneous Markov jump LPV systems

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Asynchronous H∞ control for a class of non-homogeneous Markov jump LPV systems

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Asynchronous H_∞ control for a class of non-homogeneous Markov jump LPV systems