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Journal of Applied Mathematics
Volume 2012, Article ID 859542, 20 pages
Research Article

Optimal Control for a Class of Chaotic Systems

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

Received 19 October 2011; Revised 17 January 2012; Accepted 10 February 2012

Academic Editor: Chuanhou Gao

Copyright © 2012 Jianxiong Zhang and Wansheng Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.