Optimal Disturbance Rejection with Zero Steady-State Error for Time-Delay Systems

We consider an optimal disturbance rejection problem for time-delay systems with persistent disturbances. In order to realize disturbance rejection with zero steady-state error, a disturbance compensator is constructed based on the internal model principle. At the same time, the optimal disturbance rejection problem with zero steady-state error is transformed into an optimal control problem for time-delay systems without disturbances. Then by introducing a sensitivity parameter, the original problem is reduced to solving a series of two-point boundary value (TPBV) problems without delay or advance terms. The obtained optimal control law consists of an analytic state feedback term and a compensation term, which is a series sum of the adjoint vectors. By truncating a finite terms of the adjoint vectors series, we obtain a suboptimal feedback control law with zero steady-state error. A simulation example shows the effectiveness of the presented algorithm