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

^*Corresponding author for this work

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

62 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

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

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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10.1109/TAC.2019.2915827

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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 = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2020",

month = jan,

doi = "10.1109/TAC.2019.2915827",

language = "English",

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T1 - Model Reduction of Markovian Jump Systems with Uncertain Probabilities

AU - Shen, Ying

AU - Wu, Zheng Guang

AU - Shi, Peng

AU - Ahn, Choon Ki

PY - 2020/1

Y1 - 2020/1

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

UR - https://www.scopus.com/pages/publications/85077790645

U2 - 10.1109/TAC.2019.2915827

DO - 10.1109/TAC.2019.2915827

M3 - Article

AN - SCOPUS:85077790645

SN - 0018-9286

VL - 65

SP - 382

EP - 388

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 1

M1 - 8710340

ER -

Model Reduction of Markovian Jump Systems with Uncertain Probabilities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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