Adaptive Control and Slow Manifold Analysis of a New Chaotic System

Abstract

The problem of Slow Manifold Analysis and adaptive control for a new system—-Liu system is studied in this paper. Firstly, the Liu system is considered as slow-fast autonomous dynamical system in order to obtain the equations of the slow manifold from three different ways as well as geometric characteri- zation of the attractor. And a global qualitative description of its dynamics is given. Then a brief comparison is presented among these methods. Secondly, a single new adaptive controller is designed.The analytical expression of controller and adaptive law of unknown parameters are given based on Lyapunov stability theory. With this method, parameters identification and control can be achieved simultaneously with only one controller. Numerical simulations verify the effectiveness and feasibility of the method.