Abstract
This article considers the optimal and time optimal feedback control problems for a semi-linear neutral retarded integro-differential system. The existence of mild solutions and feasible pairs for the considered system is studied by applying theory of resolvent operators for linear neutral integro-differential evolution systems, fractional powers of operators and Schauder fixed point theorem. Then the Lagrange optimal feedback control problem for the system is investigated via limit arguments under some suitable assumptions. The time optimal feedback control problem is proposed and discussed deliberately here as well. An example is presented in the end to illustrate the obtained results.
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