A New MLS Chaotic System and its Backstepping Sliding Mode Synchronization Control

Abstract

A new four-dimensional system is proposed in this paper, which is named modified Lorenz-Stenflo (MLS) system. The system is constructed by replacing one of quadratic nonlinear terms of Lorenz-Stenflo system with a piecewise linear (PWL) function. The simple structure makes the MLS system much easier to be implemented with electronic circuits. Based on adaptive control and sliding mode control methods, an adaptive sliding mode controller is derived to synchronize two MLS chaotic systems. Meanwhile the uncertain parameters in response system are identified. The error systems are deduced by backstepping method. Numerical simulations are used to verify the effectiveness of the proposed controller.