Optimal Control with Zero Steady-State Error for Time-Delay Systems with Sinusoidal Disturbances

This paper considers the optimal control for time-delay systems with sinusoidal disturbances. In order to achieve zero steady-state error, a disturbance compensator is constructed based on the internal model principle. Meanwhile the original system is transformed into an augmented system without disturbances. Then by employing the successive approximation approach, the problem of optimal control for time-delay systems can be reduced to solving a sequence of linear two-point boundary value (TPBV) problems without time-delay or time-advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original problem. The obtained control law consists of analytical feedforward and feedback terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iterative formula of adjoint vectors. A numerical example illustrates the effectiveness of the presented algorithm