A chattering-free sliding mode control design for uncertain chaotic systems

In this paper, a chattering-free sliding mode controller design for uncertain chaotic systems is presented. Since the implementation of the sliding mode control may cause a significant problem of chattering, many modified methodologies have been developed to overcome this drawback. However, each of them has own problems such as lack of robustness against disturbance variations, steady-state error, large convergence time and effect on transient performance. This paper proposes an improved sliding mode control strategy in which a modified sliding condition in a continuous function in control signal is taken into account instead of discontinuous part and also it adds an auxiliary continuous control to the control input. Then, the stability of controlled system is proved by using Lyapunov’s direct method. The usefulness of this proposed method for eliminating the chattering phenomenon in transient and steady states, in the face of uncertain chaotic systems with disturbances, is well appeared. For this purpose, the Lorenz system is studied and its simulation results are presented to demonstrate the effectiveness of the proposed control scheme.