Approximate optimal disturbance rejection for discrete timedelay systems

The optimal control for discrete time-delay systems with additive disturbances is considered. By introducing a sensitivity parameter, the original optimal disturbance rejection problem is transformed into a series of two-point boundary value problems without delay or advance terms. An iterative approximate design approach of the optimal disturbance rejection controller is derived. The optimal disturbance rejection control law obtained consists of feedforward and feedback terms and a compensation term that is the sum of the infinite series of the adjoint vectors. Using a finite sum of the series of the adjoint vectors gives a suboptimal disturbance rejection control law. A simulation example shows the optimal controller designed is robust with respect to the additive persistent disturbances.