Internal model based optimal tracking control for nonlinear discrete-time systems with sinusoidal disturbances

The optimal tracking and disturbance rejection problem for a class of nonlinear systems with sinusoidal disturbances of known frequencies in the discrete-time domain is considered. Optimal tracking and disturbance rejection can be designed separately. The original system is transformed into an augmented system without disturbances, thus the optimal rejection of disturbances can be treated by using the internal model principle (IMP) to secure asymptotic decay to zero of steady-state error. The nonlinear optimal output tracking control (OOTC) problem is solved by applying a successive approximating method. This reduces the nonlinear problem to a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems which converge in the limit to the augmented systems considered. A simulation is conducted to illustrate the effectiveness of the tracking controller.