Mathematica Eterna
Open Access

Abstract

Control of Chaotic Dynamics by Exact Linearization

M. Jana, M. Islam and N. Islam

This paper deals with an exact linearization approach to control chaos in nonlinear dynamical systems. The linearization technique has been presented as an algorithmic process to stabilize the systems at the control goal. The paper provides a unified framework for studying the two cases of having a point or a limit cycle as the control goal. A few conditions are obtained on the controller parameters that determine whether the control action guides the system asymptotically to a point or a limit cycle. The theoretical results are then applied to Sprott system N to substantiate the effectiveness of this method. The cases of both linear and non-linear output functions are studied. Numerical simulations provide some insight into the geometry of the basins of attraction of the control goal.