Chaos Control for the Unified Chaotic Systems

Abstract

Based on adaptive nonlinear feedback technique, two appropriate controllers are designed to suppress the chaotic behavior of the whole family of the generalized Lorenz system. The derived controllers have nonlinear compensator mechanisms to compensate the system nonlinearities and external disturbances. As a result the output trajectory control is accomplished. According to Lyapunov stability theory the stability analysis of the closed-loop control system is deduced. By numeric simulation, it has been shown that the designed controllers can successfully regulate the chaotic motion of the whole family of the system to a given point or make the output state to track a given bounded signal with great robustness. At the same time the required closed loop behavior is obtained. The most important effect of this letter is that under the actions of the universal controllers deduced from the adaptive technique the problem of chaos suppression of all the Lorenz-type systems can be solved successfully. Moreover the controllers have the ability of attenuating disturbances and the controller parameters are easy to tune according to rigorous analysis of stability. Based on theoretic analysis the designed controllers also provide a heuristic approach for other chaos suppression problems.