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


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 & Continuous Dynamical Systems - B, 2010, 14 (4) : 1621-1639. doi: 10.3934/dcdsb.2010.14.1621

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