This paper investigates the optimal control of a stochastic delayed system with infinite delay of general functional type. By introducing a non-anticipative path derivative and its infinite-window dual operator, we formulate the infinitely anticipated backward stochastic evolution equation (IABSEE) as the adjoint equation and establish both necessary and sufficient maximum principles. As applications, we investigate two optimal control problems featuring infinite delay. For both the classical linear-quadratic (LQ) problem and the nonlinear emission control model, the optimal controls are derived explicitly.
Guanwei Cheng (Thu,) studied this question.