Backstepping control of discrete-time chaotic systems with application to the Henon system

This brief investigates backstepping and adaptive-backstepping design for the control of a class of discrete-time chaotic systems with known or unknown parameters. The proposed method presents a systematic procedure for the control of a class of discrete-time chaotic systems. It can be used for the stabilization of discrete-time chaotic systems to a steady state as well as tracking of any desired trajectory. Moreover, dead-beat control and tracking, exact stabilization at a fixed point and tracking of any desired trajectory in finite time can be achieved. The chaotic Henon system with known or unknown parameters is taken as an example to illustrate the applicability and effectiveness of the backstepping design.