On Optimal Control Problems for Ito-Volterra States

Summary This paper presents solutions of the optimal linear-quadratic control problems for stochastic integral Ito-Volterra systems with continuous/discontinuous states. The obtained solutions are based on applying the duality principle for Volterra systems to the known solutions of the dual filtering problems for Ito-Volterra states over continuous/discontinuous observations. The optimal control laws and the gain matrix equations are first derived in the general case an Ito-Volterra state equation and then simplified in the case of a dynamic plant governed by a differential state equation.