Studies in Computational Intelligence

Abstract

This chapter investigates the control of continuous time Shimizu-Morioka chaotic system with unknown system parameters by means of three different control approaches, namely passive control, sliding mode control and backstepping design. Based on the properties of sliding mode control theory, the appropriate surfaces are designed. Lyapunov functions are used to realize that the passive controller and backstepping controllers ensure the global asymptotic stability of the system. Owing to the controllers, the Shimizu-Morioka chaotic system stabilizes towards its equilibrium points in the state space. Numerical simulations are performed to show and compare the efficiency of the proposed control methods.