Existence for Calculus of Variations and Optimal Control Problems on Time Scales

In this paper we prove the existence for optimal control problems with terminal constraints on time scales. A definition of the solution of semi-linear control systems involving Sobolev space W 1,2 T is proposed and new existence and uniqueness results of this kind of dynamic systems on time scales are presented under a weaker assumption. According to LT strong-weak lower semi-continuity of integral functionals, we establish the existence of optimal controls. In particular, the existence for calculus of variations on time scales is derived.