Fuzzy neural control of uncertain chaotic systems with backlash nonlinearity
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ORIGINAL ARTICLE
Fuzzy neural control of uncertain chaotic systems with backlash nonlinearity Da Lin • Hongjun Liu • Hong Song Fuchen Zhang
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Received: 24 April 2013 / Accepted: 14 November 2013 Springer-Verlag Berlin Heidelberg 2013
Abstract In this paper, a class of uncertain chaotic systems preceded by unknown backlash nonlinearity is investigated. Combining backstepping technique with fuzzy neural network identifying, an adaptive backstepping fuzzy neural controller (ABFNC) for uncertain chaotic systems with unknown backlash is proposed. The proposed ABFNC system is comprised of a fuzzy neural network identifier (FNNI) and a robust controller. The FNNI is the principal controller utilized for online estimation of the unknown nonlinear function. The robust controller is used to attenuate the effects of the approximation error so that the stability and control performance of the closed-loop adaptive system is achieved always. Finally, simulation results show that the ABFNC can achieve favorable tracking performances. Keywords Adaptation Chaos control Backlash nonlinearity Fuzzy neural network Identifying
1 Introduction The study of chaotic systems has been rapidly expanded during the last two decades. Many fundamental
D. Lin (&) H. Song School of Automatic and Electronic Information, Sichuan University of Science and Engineering, Zigong 643000, China e-mail: [email protected] H. Liu School of Information Engineering, Weifang Vocational College, Weifang 261041, China F. Zhang College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
characteristics can be found in a chaotic system, such as excessive sensitivity to initial conditions, broad spectrums of Fourier Transform, and fractal properties of the motion in phase space. Controlling chaotic systems has attracted a great deal of attention within the engineering society, in which different techniques have been proposed. For instance, linear state space feedback [1], Lyapunov function methods [2], adaptive control [3], and bang–bang control [4], among many others [5]. In recent years, adaptive control for uncertain nonlinear systems has received much attention based on universal function approximation, such as neural networks (NNs) or fuzzy logic systems [6–13]. Also, the application of neural networks and fuzzy logic controllers to chaotic systems has been proposed [14–18], which appears to be quite promising. Recently, the concept of incorporation fuzzy logic into a neural network has grown into a popular research topic [19]. The integrated fuzzy neural network (FNN) system possesses the merits of both fuzzy systems [20] and neural networks [21]. In this way, one can bring the low-level learning and computational power of neural networks into fuzzy systems and also high-level humanlike IF-THEN rule thinking and reasoning of fuzzy systems into neural networks. Moreover, adaptive control schemes of chaotic systems that incorporate the techniques of FNN have also grown rapidly [22–24]. Howev
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