# American Institute of Mathematical Sciences

November  2010, 14(4): 1621-1639. doi: 10.3934/dcdsb.2010.14.1621

## The optimal control to restore the periodic property of a linear evolution system with small perturbation

 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received  July 2009 Revised  December 2009 Published  August 2010

This paper concerns an optimal control problem governed by a linear evolution system with a small perturbation in the system conductivity. The system without any perturbation is assumed to have such a periodic property that it holds a periodic solution. In general, the perturbed system dose not enjoy this periodic property again, even though the perturbation has a small norm. The goal of this research is to restore the periodic property for the system, with a small perturbation, through utilizing such a control that is optimal in certain sense. It also aims to study characteristics of such an optimal control. The existence and uniqueness of the optimal control is obtained. Furthermore, a necessary and sufficient condition for the optimal control is established.
Citation: Gengsheng Wang, Guojie Zheng. The optimal control to restore the periodic property of a linear evolution system with small perturbation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1621-1639. doi: 10.3934/dcdsb.2010.14.1621
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