Adaptive sliding mode control of a class of fractional-order chaotic systems with nonlinear input

This paper deals with the problem of stabilizing a class of fractional-order chaotic systems with nonlinear input. An adaptive fractional-order sliding mode (AFSM) controller associate with time-varying feedback gains to compensate the nonlinear items of the controlled system are designed. These gains are updated through some adaptive laws, which without calculating the magnitudes of bounded nonlinear items in advance. The Lyapunov stability theory is applied to prove the stability of the closed-loop system. A simulation example is provided to verify the effectiveness and robustness of the proposed control scheme.