Optimal disturbances rejection control for a class of weak nonlinear discrete systems

A feedforward and feedback optimal control algorithm is developed for a class of weak nonlinear discrete systems affected by additive disturbances. By using the successive approximation approach (SAA), we solve the coupled nonlinear two-point boundary value (TPBV) problem derived from the necessary condition of the optimal control problem. The main result concerns the existence and design of a feedforward and feedback optimal control law. The optimal control law obtained consists of an accurate feedback term, a feedforward compensation term and a nonlinear compensation term. The feedback and the feedforward terms can be obtained by solving a Riccati equation and a Slyester equation respectively. The nonlinear term can be approximated via adjoint vector sequences. Also, a disturbances observer is constructed to make the optimal control law physically realizable. The validity of the algorithm is showed by an example.