Continuous-time single network adaptive critic based optimal sliding mode control for nonlinear control affine systems

Integrating the Sliding Mode Control (SMC) theory with Approximate Dynamic Programming (ADP), this paper presents a novel technique for designing robust optimal sliding mode control schemes for a class of nonlinear control affine systems with disturbances. The main motivation of the work is to merge the inherent robustness of conventional sliding mode control with optimal control theory. Towards this end, a dynamic sliding surface is first used and a control law is defined which guarantees stability in the sense of Lyapunov in the presence of the disturbances. Next, a continuous time single network adaptive critic is used to find an approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. Since the adaptive critic approximates the optimal cost-to-go function using a parametric positive semi-definite function, the stability of the system is studied during the evolution of weights by employing Lyapunov theory. The merits of the proposed algorithm are demonstrated through simulation examples.