Optimal sliding mode design for nonlinear discrete-time systems

The optimal sliding mode control (OSDC) for nonlinear discrete-time systems with infinite horizon quadratic performance indexes is considered. The optimal control law for general nonlinear system with quadratic index is given in terms of solution to the HJB(Hamilton-Jocabi-Bellman) equation or the nonlinear TPBV (Two Point Boundary Problem) problem. In the optimal sliding surface designing process, this paper explores the successive approximation approach (SAA). The OSDC obtained consists of linear analytic functions and a compensation term which is a series sum of adjoint vectors. The results of the simulation show the validity of the approach mentioned.