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FUZZY MODELING AND CONTROL OF CHAOTIC SYSTEMS Chaotic behavior is a seemingly random behavior of a deterministic system that is characterized by sensitive dependence on initial conditions. Chaotic behavior of a physical system can either be desirable or undesirable, depending on the application. It can be beneficial in many circumstances, such as enhanced mixing of chemical reactants. Chaos can, on the other hand, entail large-amplitude motions and oscillations that might lead to system failure | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTER 9 ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic FUZZY MODELING AND CONTROL OF CHAOTIC SYSTEMS Chaotic behavior is a seemingly random behavior of a deterministic system that is characterized by sensitive dependence on initial conditions. Chaotic behavior of a physical system can either be desirable or undesirable depending on the application. It can be beneficial in many circumstances such as enhanced mixing of chemical reactants. Chaos can on the other hand entail large-amplitude motions and oscillations that might lead to system failure. The OGY method 1 2 for controlling chaos sparked a great number of schemes on controlling chaos in linear and or nonlinear control frameworks . 3 9 . In this chapter we explore the interaction between fuzzy control systems and chaos. First we show that fuzzy modeling techniques can be used to model chaotic dynamical systems which also implies that fuzzy systems can be chaotic. This is not surprising given the fact that fuzzy systems are essentially nonlinear. On the subject of controlling chaos this chapter presents a unified approach 10 - 14 using the LMI-based fuzzy control system design. Up to this point of the book we have mostly considered the regulation problem in control systems. Regulation is no doubt one of the most important problems in control engineering. For chaotic systems however there are a number of interesting nonstandard control problems. In this chapter we develop a unified approach to address some of these problems including stabilization synchronization and chaotic model following control CMFC for chaotic systems. A cancellation technique CT is presented as a main result for stabilization. The CT also plays an important role in synchronization and chaotic model following control. Two cases are considered in synchronization. The first one deals with the .

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