Comparison between chaos-control methods efficiency for discrete systems

Abstract

Controlling unstable behaviour of many nonlinear dynamical systems is one of the recent interesting topics for researchers. Many methods are proposed to stabilize chaotic discrete time systems. In this paper, a comparison between different control methods is performed for distinguishing their efficiency. The used control methods are Ott-Grebogi-Yorke (OGY), Predictive Feedback Control (PFC), Time Delay Auto Synchronization (TDAS) and its extended (ETDAS), control methods based on self-organizing migrating algorithm (SOMA) and differential evolution (DE). They are briefly introduced and then applied to most popular discrete nonlinear systems 100 times. The controlled orbits of period-1 characteristics are evaluated, presenting the robust of each method according to autocorrelation, the number of required iterations, number of successfully controlled orbits, and max absolute value of the control input. TDAS and PFC methods are the most convenient to stabilize the chaotic attractor of the system.