Fast convergence control of a class of uncertain chaotic systems with input nonlinearity by using a new sliding mode controller

Abstract

This paper studies the fast stability of a class of 3-D chaotic systems in the presence of uncertainties, disturbances as well as input nonlinearity. Some original contributions are concluded: Firstly, this work introduces a special nonlinear input function and a fast convergence system which can be utilized to design controller and sliding mode, respectively. Secondly, a systematic design scheme is derived to ensure the fast stability of subsystem and several virtual controllers are obtained by means of backstepping method. Thirdly, considering the existence of compound disturbances, a new sliding mode is constructed to improve robustness of the controlled systems. Fourthly, by combining nonlinear input function with sliding mode control theory, a new controller is devised and some sufficient conditions of fast convergence control for the 3D chaotic system are derived. There are two features of the presented control criterion: (1) The convergence rate of state trajectories to the origin can be adjusted in advance by choosing the explicit parameters. (2) The time of state trajectories that move toward the sliding surface is finite and bounded by a constant. Numerical results are carried out by employing the Jerk chaotic system to testify the effectiveness of the proposed scheme.