Control of chaos: Lie algebraic exact linearization approach for the Lü system

Abstract

In this article, nonlinear control of the Lu chaos is presented by transforming a Lu system in a linear controllable system by using the Lie algebraic exact linearization method. Numerically, control of chaos does not have much place in current literature unless one actually finds and displays the controller in the chaotic system. The controller for the Lu system is designed for an arbitrary output. Based on this controller, both linear and nonlinear outputs are discussed in detail. Numerical simulations are carried out for all necessary aspects of the Lu problem that justify our analytical findings. Moreover, the stabilization of the Lu system based on the linear controllable system is discussed in the form of limit cycles and Hopf bifurcation. In particular, the numerical Hopf bifurcation diagram is presented using the numerical continuation technique.