Optimal Control for a Class of Chaotic Systems

Optimal Control for a Class of Chaotic Systems

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal con...

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Main Authors: Jianxiong Zhang, Wansheng Tang
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/859542
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spelling doaj-0307b4a9042f40c7ac449718794aec152020-11-25T00:12:49ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/859542859542Optimal Control for a Class of Chaotic SystemsJianxiong Zhang0Wansheng Tang1Institute of Systems Engineering, Tianjin University, Tianjin 300072, ChinaInstitute of Systems Engineering, Tianjin University, Tianjin 300072, ChinaThis paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.http://dx.doi.org/10.1155/2012/859542
collection DOAJ
language English
format Article
sources DOAJ
author Jianxiong Zhang
Wansheng Tang
spellingShingle Jianxiong Zhang
Wansheng Tang
Optimal Control for a Class of Chaotic Systems
Journal of Applied Mathematics
author_facet Jianxiong Zhang
Wansheng Tang
author_sort Jianxiong Zhang
title Optimal Control for a Class of Chaotic Systems
title_short Optimal Control for a Class of Chaotic Systems
title_full Optimal Control for a Class of Chaotic Systems
title_fullStr Optimal Control for a Class of Chaotic Systems
title_full_unstemmed Optimal Control for a Class of Chaotic Systems
title_sort optimal control for a class of chaotic systems
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.
url http://dx.doi.org/10.1155/2012/859542
work_keys_str_mv AT jianxiongzhang optimalcontrolforaclassofchaoticsystems
AT wanshengtang optimalcontrolforaclassofchaoticsystems
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