Fuzzy Chaotic Systems: Modeling, Control, and ApplicationsBringing 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
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 |
284 | |
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Common terms and phrases
adaptive applied approach approximation Assume attractor Banach spaces becomes behavior bifurcation bounded called changes chaos chaotic systems chapter ciphertext close compact complex connections Consider constant continuous continuous-time controlled system defined definition denoted derived described determine discrete-time discretized dynamics eigenvalues equation error examples exists fixed point function fuzzy control fuzzy logic fuzzy model fuzzy rules fuzzy sets fuzzy system gain given global inference initial input introduced linear linguistic Lorenz system mathematical matrix means membership functions method neighborhood nonlinear Note obtained operations origin oscillator output parameters periodic orbits phase positive problem proof properties proposed region regular relations represented respectively response rules satisfying shown in Fig shows signal simulation space stable structure synchronization techniques Theorem trajectory uncertainties universe unstable values variables varied zero
Popular passages
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.