Optimal disturbance rejection with zero steady-state error for nonlinear systems with sinusoidal disturbances

In this paper, an optimal disturbance rejection technique is proposed for a class of nonlinear systems affected by the external sinusoidal disturbances. In this technique, we first transform the given nonlinear system into an augmented system without any disturbance. Then by choosing an infinite-time quadratic cost functional, the problem of optimal disturbance rejection is reduced into the problem of finding an optimal control law for the nonlinear augmented system. Finally, in order to approximate the optimal control law for the derived system, an iterative algorithm based on the modal series method is designed. The convergence analysis of the proposed method is studied. Comparative results demonstrate the efficiency and high accuracy of the suggested technique.