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Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 49J20; Secondary: 49J27.

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