Optimal control and synthesis of nonlinear infinite dimensional systems

In this paper, optimal control problems of nonlinear distributed systems in Banach spaces with a general criterion functional are considered. The maximum principle as a necessary condition for an optimal process is proved forthright by the approach of analysis of the oscillating variations of control. It is shown that value functions are locally Lipschitz continuous. By using lower Dini derivatives, a general synthesis result on optimal feedback control via solving a differential inclusion is obtained.