Approximate Design of Optimal Output Tracking Controller for Time-Delay Systems with Sinusoidal Disturbances

This paper addresses the problem of optimal output tracking control (OOTC) for linear discrete-time systems, with simultaneous rejection of sinusoidal disturbances. The systems are transformed into a sequence of linear two-point boundary value (TPBV) problems. The optimal tracking control law consists of accurate linear terms and a limit of a sequence of adjoint compensation terms, which are derived by using the successive approximation approach (SAA). A suboptimal tracking control law is obtained by taking the finite-step iteration of the compensation sequence. A numerical example indicates that the algorithm is effective and robust with respect to sinusoidal disturbances