OPTIMAL FEEDBACK CONTROL RESULTS FOR A SECOND-ORDER EVOLUTION SYSTEM WITH FINITE DELAY

This article considers the optimal and time optimal feedback control problems for a semi-linear retarded second-order system. The existence and uniqueness of mild solutions and feasible pairs for the considered system are first studied by applying theory of cosine family of linear operators and Banach fixed point theorem. Then sufficient conditions of the Lagrange optimal feedback control problem for the system are obtained under some suitable assumptions via limit arguments. The time optimal feedback control problem is also proposed and investigated deliberately here. An example is presented in the end to illustrate the applications of the obtained results.