Abstract
This paper concerns an optimal control problem governed by alinear evolution system with a small perturbation in the systemconductivity. The system without any perturbation is assumed to havesuch a periodic property that it holds a periodic solution. Ingeneral, the perturbed system dose not enjoy this periodicproperty again, even though the perturbation has a small norm. Thegoal of this research is to restore the periodic property for thesystem, with a small perturbation, through utilizing such a controlthat is optimal in certain sense. It also aims to studycharacteristics of such an optimal control. The existence anduniqueness of the optimal control is obtained. Furthermore, anecessary and sufficient condition for the optimal control isestablished.
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