Optimal Stochastic Disturbance Rejection Design for Discrete-time Systems with Time-delay

Optimal control for discrete-time systems with time-delay affected by additive stochastic disturbances is considered. By introducing a sensitivity parameter, we transform the original optimal disturbance rejection control (ODRC) problem into a series of two-point boundary value (TPBV) problems without time-delay and time-advance terms. The approximate ODRC law consists of analytic state feedback and feedforward terms and a compensation term in a series form. The compensation term can be obtained with an iterated formula of the adjoint vectors. Physical realization of the approximate ODRC law is solved by using a state estimator. Simulation results show the approach in this paper is more robust with respect to exogenous persistent disturbances.