A second-order maximum principle for singular optimal controls with recursive utilities of stochastic delay systems

摘要

This paper is devoted to the investigation of the second-order necessary conditions of singular control problems for controlled forward-backward delay systems in the case where the control domain is non-convex and the diffusion coefficients are independent of control. A second-order matrix-valued adjoint system is constructed to solve the obstacle caused by the product of the solution and its delay counterpart of the first-order variational equations. With the help of this observation, the second-order expansion of cost functional Y-epsilon and the stochastic maximum principle are proved. Our work generalizes the classical case to the delay case (C) 2019 European Control Association. Published by Elsevier Ltd. All rights reserved.