Chaos control of new Mathieu-van der Pol systems by fuzzy logic constant controllers

Abstract

In this paper, a new fuzzy logic controller-fuzzy logic constant controller (FLCC) is introduced to chaotic signals controlling. The main ideas of the FLCC are described as follows: (1) proving the two chaotic systems are going to achieve asymptotically stable via Lyapunov direct method; (2) via detecting the sign of the errors, the appropriate fuzzy logic control scheme is operated; (3) choosing the upper bound and the lower bound of the error derivatives of the chaotic signals to be the consequent parts (corresponding controllers). Due to controllers in traditional method - derived by Lyapunov direct method, are always complicated, nonlinear form or the functions of errors, a new simplest controller-FLCC is presented in this paper to synchronize two chaotic signals. Through the FLCC, there are three main contributions can be obtained: (1) the mathematical models of the nonlinear chaotic systems can be unknown, all we have to do is capturing the signals of the unknown systems; (2) through the fuzzy logic rules, the strength of controllers can be adjusted via the corresponding membership functions (which are decided by the values of error derivatives); (3) by the FLCC, the chaotic system can be much more exactly and efficiently controlled to the trajectory of our goal than traditional ones. Three cases, original point, regular function and chaotic Qi system (with large values of initial conditions), are given to illustrate the effectiveness of our new FLC. (C) 2011 Elsevier B.V. All rights reserved.