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Top1. Introduction
In recent years, fractional calculus deals with derivatives and integrations of arbitrary order (Samko et al., 1993; Kilbas et al., 2006) and numerous applications of fractional order systems in many areas of science and engineering have been proposed such as control theory, electromagnetic waves, viscoelastic systems, diffusion signal processing and bio-engineering (Vanagre & Feliu, 2002; Hilfer, 2001). It is observed that the description of some systems is more accurate when the fractional derivative is used. Nowadays, many fractional-order differential systems behave chaotically, such as the fractional-order Chua’s system (Hartley et al., 2001) the fractional-order Duffing system (Gao & Yu, 2005) the fractional-order Lu system (Deng & Li, 2005), the fractional-order Chen’s system (Lu & Chen, 2006), the fractional-order cellular neural network (Petra, 2006) the fractional-order neural network (Zhou et al., 2006).
Owing to its potential applications in secure communication and control processing (Matigon, 1996), study of chaos tracking, synchronization, in fractional order dynamical systems and related phenomena is receiving growing attention (Kinai et al., 2009; Grigorenko, 2003). The tracking problem of fractional order chaotic systems is first investigated by Deng and Li (2005) who carried out tracking in case of the two fractional Lü systems. Afterwards, they studied chaos tracking of the Chen system with a fractional order in a different manner (Li & Peng, 2004; Li & Chen, 2003; Deng & Lin, 2005).
Furthermore, the advent of fuzzy set techniques provides us with a powerful tool to solve demanding real word problem with uncertain and unpredictable environments. Based on the universal approximation theorem (Wang, 1993, 1994; Wang & Mendel, 1992; Hwang & Lin, 1992) (fuzzy logic controllers are general enough to perform any nonlinear control actions), there is rapidly growing interest in systematic design methodologies for a class of nonlinear systems using fuzzy adaptive control schemes. By equipping with a training algorithm an adaptive fuzzy controller is synthesized from a collection of fuzzy IF-THEN rules and the parameters of the membership functions characterizing the linguistic terms in the IF-THEN rules changed according to some adaptive law for the purpose of controlling a plant to track a reference trajectory.