A Class of Optimal Control Problems on Time Scales

This paper is mainly concerned with a class of optimal control problem of systems governed by dynamic systems on time scales. Discussing L1-strong-weak lower semicontinuity of integral functional on time scales, we give sufficient conditions on the existence of optimal controls for control sets Uad⊂L1 (Y, R). In addition, studying the weak solution of backward problem for dynamic equations on time scales, the necessary conditions of optimality are derived.