Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems

Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems

Abstract In this article, robust static output feedback (SOF) Nash games for a class of uncertain Markovian jump linear stochastic systems (UMJLSSs) are investigated, in which each player may have access to local/private SOF information. It is proved that the robust SOF Nash strategy set can be obta...

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Main Authors: Hiroaki Mukaidani, Hua Xu, Weihua Zhuang
Format: Article
Language:English
Published: Wiley 2021-07-01
Series:IET Control Theory & Applications
Online Access:https://doi.org/10.1049/cth2.12143
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spelling doaj-01f0cda08ca9453092b452e503ae77222021-08-19T09:15:34ZengWileyIET Control Theory & Applications1751-86441751-86522021-07-0115111559157010.1049/cth2.12143Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systemsHiroaki Mukaidani0Hua Xu1Weihua Zhuang2Graduate School of Advanced Science and Engineering Hiroshima University Kagamiyama JapanGraduate School of Business Sciences The University of Tsukuba Tokyo JapanDepartment of Electrical and Computer Engineering University of Waterloo Ontario CanadaAbstract In this article, robust static output feedback (SOF) Nash games for a class of uncertain Markovian jump linear stochastic systems (UMJLSSs) are investigated, in which each player may have access to local/private SOF information. It is proved that the robust SOF Nash strategy set can be obtained by minimizing the upper bounds of the cost functions based on a guaranteed cost control mechanism. By using the Karush–Kuhn–Tucker (KKT) condition, the necessary conditions for the existence of the robust SOF Nash strategy set are established in terms of the solvability conditions of nonlinear simultaneous algebraic equations (NSAEs). A heuristic algorithm is developed to solve the NSAEs. Particularly, it is shown that the robust convergence of the heuristic algorithm is guaranteed by combining the Krasnoselskii–Mann (KM) iterative algorithm with a new convergence condition. Finally, a simple practical example is presented to show the reliability and usefulness of the proposed algorithm.https://doi.org/10.1049/cth2.12143
collection DOAJ
language English
format Article
sources DOAJ
author Hiroaki Mukaidani
Hua Xu
Weihua Zhuang
spellingShingle Hiroaki Mukaidani
Hua Xu
Weihua Zhuang
Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
IET Control Theory & Applications
author_facet Hiroaki Mukaidani
Hua Xu
Weihua Zhuang
author_sort Hiroaki Mukaidani
title Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
title_short Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
title_full Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
title_fullStr Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
title_full_unstemmed Robust static output feedback Nash strategy for uncertain Markov jump linear stochastic systems
title_sort robust static output feedback nash strategy for uncertain markov jump linear stochastic systems
publisher Wiley
series IET Control Theory & Applications
issn 1751-8644
1751-8652
publishDate 2021-07-01
description Abstract In this article, robust static output feedback (SOF) Nash games for a class of uncertain Markovian jump linear stochastic systems (UMJLSSs) are investigated, in which each player may have access to local/private SOF information. It is proved that the robust SOF Nash strategy set can be obtained by minimizing the upper bounds of the cost functions based on a guaranteed cost control mechanism. By using the Karush–Kuhn–Tucker (KKT) condition, the necessary conditions for the existence of the robust SOF Nash strategy set are established in terms of the solvability conditions of nonlinear simultaneous algebraic equations (NSAEs). A heuristic algorithm is developed to solve the NSAEs. Particularly, it is shown that the robust convergence of the heuristic algorithm is guaranteed by combining the Krasnoselskii–Mann (KM) iterative algorithm with a new convergence condition. Finally, a simple practical example is presented to show the reliability and usefulness of the proposed algorithm.
url https://doi.org/10.1049/cth2.12143
work_keys_str_mv AT hiroakimukaidani robuststaticoutputfeedbacknashstrategyforuncertainmarkovjumplinearstochasticsystems
AT huaxu robuststaticoutputfeedbacknashstrategyforuncertainmarkovjumplinearstochasticsystems
AT weihuazhuang robuststaticoutputfeedbacknashstrategyforuncertainmarkovjumplinearstochasticsystems
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