Fuzzy Chaotic Systems: Modeling, Control, and Applications

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Springer, Aug 2, 2006 - Computers - 300 pages
Bringing together the two seemingly unrelated concepts,fuzzy logic andchaos theory,isprimarilymotivatedbytheconceptofsoft computing (SC),initiated by Lot? A. Zadeh, the founder of fuzzy set theory. The principal constituents of SC are fuzzy logic (FL), neural network theory (NN) and probabilistic reasoning (PR), with the latter subsuming parts of belief networks, genetic algorithms, chaos theory and learning theory. What is important to note is that SC is not a melange of FL, NN and PR. Rather, it is an integration in which each of the partners contributes a distinct methodology for addressing problems in their common domain. In this perspective, the principal cont- butions of FL, NN and PR are complementary rather than competitive. SC di?ers from conventional (hard) computing in that it is tolerant of imprecision, uncertainty and partial truth. In e?ect, the role model for soft computing is the human mind. From the general SC concept, we extract FL and chaos theory as the object of this book to study their relationships or interactions. Over the past few decades, fuzzy systems technology and chaos theory have received ever increasing research interests from, respectively, systems and control engineers, theoretical and experimental physicists, applied ma- ematicians, physiologists, and other communities of researchers. Especially, as one of the emerging information processing technologies, fuzzy systems technology has achieved widespread applications around the globe in many industriesandtechnical?elds,rangingfromcontrol,automation,andarti?cial intelligence (AI) to image/signal processing and pattern recognition. On the otherhand,inengineeringsystemschaostheoryhasevolvedfrombeingsimply a curious phenomenon to one with real, practical signi?cance and utilization.
 

Contents

Introduction
1
Fuzzy Logic and Fuzzy Control 13
12
Chaos and Chaos Control
31
Definition of Chaos in Metric Spaces of Fuzzy Sets
53
Fuzzy Modeling of Chaotic Systems I Mamdani Model
73
Fuzzy Modeling of Chaotic Systems II TS Model 91
90
Fuzzy Control of Chaotic Systems I Mamdani Model
121
Adaptive Fuzzy Control of Chaotic Systems
142
Synchronization of TS Fuzzy Systems 189
188
Chaotifying TS Fuzzy Systems
205
Intelligent Digital Redesign for TS Fuzzy Systems
239
Spatiotemporal Chaos and Synchronization
254
Fuzzychaosbased Cryptography
275
References 285
284
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Page 293 - On Stability of Fuzzy Systems Expressed by Fuzzy Rules with Singleton Consequents", IEEE Trans, on Fuzzy Systems, vol.
Page vii - SC is not a melange of FL, NN and PR. Rather; it is a partnership in which, each of the partners contributes a distinct methodology for addressing problems in its domain. In this perspective, the principal contributions of FL, NN and PR are complementary rather than competitive.
Page vii - Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind.
Page vii - At this juncture, the principal constituents of soft computing (SC) are fuzzy logic (FL), neural network theory (NN), and probabilistic reasoning (PR), with the latter subsuming belief networks, genetic algorithms, chaos theory, and parts of learning theory. What is important to note is that SC is not a melange of FL, NN, and PR. Rather, it is a partnership in which each of the partners contributes a distinct methodology for addressing problems in its domain. In this perspective...
Page 293 - Stable adaptive fuzzy control of nonlinear systems,", IEEE Trans.