Maximum principle for partially-observed optimal control problems of stochastic delay systems

This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov’s theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.