Optimal control theory for dynamic equations

Abstract

In this work we propose an investigation of the existence of solutions to optimal control problems in time scales. Two classes of optimal control problems governed by nonlinear first order dynamic equations on time scales are studied. One of the classes of problems studied relies optimal control problems present in the time scales literature, more specifically, we propose an extension of problems present in the literature. As for the other class of problems studied the states are absolutely continuous, and we proceed with an approach similar to that of the optimal control problems in continuous time to obtain the existence of solutions.