Two Problems In Optimal Control Theory And Applications

This thesis consists of three parts.In the first part, we introduce the two problems which will be discussed in the following two parts and the main results of the thesis.In the second part, we discuss the time-optimal control problem for an ordinary differential system with a pointwise state-constraint. We give the explicit solution.Finally in the third part, we study the optimal control problems for the variational inequality with delays in the highest order spatial derivatives. Under some suitable conditions, we prove the existence and the maximum principle for the optimal control.