Parameter identification and backstepping design of synchronization controller for uncertain chaotic system

Abstract

A parameter observer is designed to identify Rossler system with unknow parameters. Chaos synchronization between uncertain Rossler system and Coullet system is realized via backstepping method.The synchronization controller is presented based on stability theory, and the area of controlling gain is determined. The simulation results show that all the state variables in the Coullet system can track any desired trajectory in the Rossler system exactly when the parameter observer and backstepping controller are functioning, which shows the method is effective and feasible.

Synchronisation of chaotic systems using a novel sampled-data fuzzy controller

“…Referring to error system (7), synchronisation is achieved if e(t) → 0 as time goes by. Here, LMI-based synchronisation conditions are derived to guarantee synchronisation by using a new parameter-dependent Lyapunov-Krasovskii functional.…”

“…According to the Newton-Leibniz formula and the error system in system (7), with appropriately dimensional matrices M (t), N (t) defined in Eq. ( 8), we have…”

“…Those LMIs ( 9)-( 11) are derived. In other words, LMIs ( 9)-( 12) are the stability conditions to guarantee error system (7). Moreover, the feedback gains matrices could be attained by G j = F j Ω −1 , j = 1, 2, .…”

“…Remark 2 As stated system (7), the term m e (x(t) is bounded as w i (x(t)), ŵj ( x(t)) and x(t) are bounded. For most actual settings, the membership functions w i (x(t)), ŵj ( x(t)) are known for the underlying chaotic fuzzy systems and hence the value of ρ in inequality (17) can be calculated as follows:…”

Passive control and synchronization of hyperchaotic Chen system

“…Since the chaos control and synchronization was first introduced by Pecora and Carroll, [1,2] it has been an active research topic in nonlinear science, and has been extensively studied. In the past two decades, a variety of approaches have been proposed for the chaos synchronization, including manifold-based method, [3] adaptive method, [4] time delay feedback approach, [5] backstepping method, [6] nonlinear control scheme [7,8] and many others. Recently, the concept of passivity [9] of nonlinear systems has aroused the new interest in nonlinear control field.…”