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DCDS-B

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.

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