An approximate optimal tracking control algorithm of nonlinear systems for sinusoidal disturbances rejection

An approximate optimal tracking control (OTC) algorithm for sinusoidal disturbances rejections of nonlinear systems is developed in this paper. In the proposed control method, the nonlinear two-point boundary value (TPBV) problem, which is derived from the original OTC problem, is rewritten into a new form through a transformation and is transformed into a sequence of linear TPBV problems by using the successive approximation approach. Then the OTC law is obtained from the proposed iterative method successively, which consists of analytic linear feedforward and feedback terms and the limit of a compensation sequence of adjoint vectors. The feedforward term is used to cancel sinusoidal disturbances and the adjoint vectors sequence is the compensation for nonlinearities. A reference input observer is constructed to obtain a physically realizable feedforward controller. And by truncating a finite term of the adjoint vectors sequence, an approximate OTC law is obtained. Numerical simulations are employed to test the effectiveness of the proposed algorithm.