Optimal Control Problem for a Class of Non-autonomous Stochastic Integro-differential Equations

In order to study the optimal control problem of a class of non-autonomous stochastic integro-differential equation in Hilbert space, the existence theorem of mild solution of the problem is established by using stochastic analysis, theories of operator semigroups and Sadovskii fixed point theorem. On this basis, the existence of the optimal state-control pair is discussed by constructing minimization sequences twice.