A Novel Linear Feedback Control Approach of Lorenz Chaotic System

Abstract

In chaos control fields, the nonfeedback and the nonlinear feedback approaches are inevitable much less flexible. However linear feedback controllers are easy to implement, especially in electrical systems. In this paper, based on linear feedback control strategy and Lyapunov stability theory, some effective linear feedback controllers of variable states are given which can realize the control purposes of unstable equilibriums by a dislocated adaptive control of variables x and y. A numerical example is given to illuminate the design procedure and advantage of the results derived. It is noted that in principle, the dislocated adaptive control approaches developed in this paper can be applied to general smooth chaotic systems satisfying some mild required properties such as Chen system, lu system, etc.