Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a...

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Main Authors: Lifan Kang, Yue Wang, Ting Hou
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/1940676
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spelling doaj-691ceafb193045eb8cfad0c7cf6c26572020-11-25T03:50:10ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/19406761940676Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition ProbabilitiesLifan Kang0Yue Wang1Ting Hou2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaDivision of Public Teaching, Jinan Vocational College, Jinan 250103, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan 250358, ChinaThis note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.http://dx.doi.org/10.1155/2020/1940676
collection DOAJ
language English
format Article
sources DOAJ
author Lifan Kang
Yue Wang
Ting Hou
spellingShingle Lifan Kang
Yue Wang
Ting Hou
Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
Mathematical Problems in Engineering
author_facet Lifan Kang
Yue Wang
Ting Hou
author_sort Lifan Kang
title Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
title_short Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
title_full Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
title_fullStr Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
title_full_unstemmed Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities
title_sort robust control for nonlinear markov jump systems with partially unknown transition probabilities
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.
url http://dx.doi.org/10.1155/2020/1940676
work_keys_str_mv AT lifankang robustcontrolfornonlinearmarkovjumpsystemswithpartiallyunknowntransitionprobabilities
AT yuewang robustcontrolfornonlinearmarkovjumpsystemswithpartiallyunknowntransitionprobabilities
AT tinghou robustcontrolfornonlinearmarkovjumpsystemswithpartiallyunknowntransitionprobabilities
_version_ 1715106825133621248

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