Model Reduction of Markovian Jump Systems with Uncertain Probabilities

Ying Shen; Zheng Guang Wu; Peng Shi; Choon Ki Ahn

doi:10.1109/TAC.2019.2915827

Model Reduction of Markovian Jump Systems with Uncertain Probabilities

Ying Shen, Zheng Guang Wu, Peng Shi, Choon Ki Ahn

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

This paper studies the problem of model reduction for nonhomogeneous Markovian jump systems. The transition probability matrix of the nonhomogeneous Markovian chain has the characteristic of a polytopic structure. An asynchronous reduced-order model is considered, and the asynchronization is modeled by a hidden Markov model with a partially unknown conditional probability matrix. Under this framework, a new sufficient condition is proposed to ensure that the augmented system is stochastically mean-square stable with a specified level of H-infty performance. Finally, a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained.

Original language	English
Article number	8710340
Pages (from-to)	382-388
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	65
Issue number	1
DOIs	https://doi.org/10.1109/TAC.2019.2915827
Publication status	Published - 2020 Jan

Keywords

Asynchronization
hidden Markov model
model reduction
nonhomogeneous Markovian chain
partially unknown conditional probabilities

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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title = "Model Reduction of Markovian Jump Systems with Uncertain Probabilities",

abstract = "This paper studies the problem of model reduction for nonhomogeneous Markovian jump systems. The transition probability matrix of the nonhomogeneous Markovian chain has the characteristic of a polytopic structure. An asynchronous reduced-order model is considered, and the asynchronization is modeled by a hidden Markov model with a partially unknown conditional probability matrix. Under this framework, a new sufficient condition is proposed to ensure that the augmented system is stochastically mean-square stable with a specified level of H-infty performance. Finally, a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained.",

keywords = "Asynchronization, hidden Markov model, model reduction, nonhomogeneous Markovian chain, partially unknown conditional probabilities",

author = "Ying Shen and Wu, {Zheng Guang} and Peng Shi and Ahn, {Choon Ki}",

note = "Funding Information: Manuscript received January 23, 2019; accepted April 20, 2019. Date of publication May 9, 2019; date of current version December 27, 2019. This work was supported in part by the Science Fund for Creative Research Groups under Grant 61621002, in part by the National Nature Science Foundation of China under Grant 61773131 and Grant U1509217, and in part by the Australian Research Council under Grant DP170102644. Recommended by Associate Editor P. Rapisarda. (Corresponding author: Zheng-Guang Wu.) Y. Shen and Z.-G. Wu are with the State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China (e-mail:, yingshen@zju.edu.cn; nashwzhg@zju.edu.cn).",

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doi = "10.1109/TAC.2019.2915827",

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AU - Shi, Peng

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N1 - Funding Information: Manuscript received January 23, 2019; accepted April 20, 2019. Date of publication May 9, 2019; date of current version December 27, 2019. This work was supported in part by the Science Fund for Creative Research Groups under Grant 61621002, in part by the National Nature Science Foundation of China under Grant 61773131 and Grant U1509217, and in part by the Australian Research Council under Grant DP170102644. Recommended by Associate Editor P. Rapisarda. (Corresponding author: Zheng-Guang Wu.) Y. Shen and Z.-G. Wu are with the State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China (e-mail:, yingshen@zju.edu.cn; nashwzhg@zju.edu.cn).

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N2 - This paper studies the problem of model reduction for nonhomogeneous Markovian jump systems. The transition probability matrix of the nonhomogeneous Markovian chain has the characteristic of a polytopic structure. An asynchronous reduced-order model is considered, and the asynchronization is modeled by a hidden Markov model with a partially unknown conditional probability matrix. Under this framework, a new sufficient condition is proposed to ensure that the augmented system is stochastically mean-square stable with a specified level of H-infty performance. Finally, a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained.

AB - This paper studies the problem of model reduction for nonhomogeneous Markovian jump systems. The transition probability matrix of the nonhomogeneous Markovian chain has the characteristic of a polytopic structure. An asynchronous reduced-order model is considered, and the asynchronization is modeled by a hidden Markov model with a partially unknown conditional probability matrix. Under this framework, a new sufficient condition is proposed to ensure that the augmented system is stochastically mean-square stable with a specified level of H-infty performance. Finally, a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained.

KW - Asynchronization

KW - hidden Markov model

KW - model reduction

KW - nonhomogeneous Markovian chain

KW - partially unknown conditional probabilities

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Model Reduction of Markovian Jump Systems with Uncertain Probabilities

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