Optimal sliding mode design for nonlinear systems

This paper designs a time-varying nonlinear switching manifold in an optimal fashion for a class of nonlinear systems by developing the successive approximation approach of differential equation into infinite-time horizon. Based on the reaching law approach, we obtain a reach the nonlinear sliding surface. The stability of the nonlinear sliding mode is analyzed. The convergence velocity of every state trajectory on the ideal sliding surface can be adjusted through choosing quadratic performance index Simulation example is employed to test the validity of the proposed design algorithm.