Li Fuzzy Chaotic Systems

Modeling, Control, and Applications
1. Auflage 2006
ISBN: 978-3-540-33221-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 199, 323 Seiten, eBook

Reihe: Studies in Fuzziness and Soft Computing

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 andutilization.

Zielgruppe

Research

Autoren/Hrsg.

Li, Zhong

Inhaltsverzeichnis

Fuzzy Logic and Fuzzy Control.- Chaos and Chaos Control.- Definition of Chaos in Metric Spaces of Fuzzy Sets.- Fuzzy Modeling of Chaotic Systems – I (Mamdani Model).- Fuzzy Modeling of Chaotic Systems – II (TS Model).- Fuzzy Control of Chaotic Systems – I (Mamdani Model).- Adaptive Fuzzy Control of Chaotic Systems (Mamdani Model).- Fuzzy Control of Chaotic Systems – II (TS Model).- Synchronization of TS Fuzzy Systems.- Chaotifying TS Fuzzy Systems.- Intelligent Digital Redesign for TS Fuzzy Systems.- Spatiotemporal Chaos and Synchronization in Complex Fuzzy Systems.- Fuzzy-chaos-based Cryptography.

Leseproben

2 Fuzzy Logic and Fuzzy Control (Sp. 13-14)

Over the past few decades, there has developed a tremendous amount of literature on the theory of fuzzy set and fuzzy control. This chapter attempts to sketch the contours of fuzzy logic and fuzzy control for the readers, who may have no knowledge in this ?eld, with easy-to-understand words, avoiding abstruse and tedious mathematical formulae.

2.1 Introduction

Fuzzy logic is in nature an extension of conventional (Boolean) logic to handle the concept of partial truth – truth values between “completely true” and “completely false”. It was introduced by Lot? Zadeh in 1965 as a means to model the uncertainty of natural language.

Fuzzy logic in the broad sense, which has been better known and extensively applied, serves mainly as a means for fuzzy control, analysis of vagueness in natural language and several other application domains. It is one of the techniques of soft-computing, i.e. computational methods tolerant to suboptimality and impreciseness (vagueness) and giving quick, simple and sufficiently good solutions [48, 49, 50, 51].

Fuzzy logic in the narrow sense is a symbolic logic with a comparative notion of truth developed fully in the spirit of classical logic (syntax, semantics, axiomatization, truth-preserving deduction, completeness, and propositional and predicate logic). It is a branch of many-valued logic based on the paradigm of inference under vagueness. This fuzzy logic is a relatively young discipline, not only serving as a foundation for the fuzzy logic in a broad sense but also of independent logical interest, since it turns out that strictly logical investigation of this kind of logical calculi can go rather far [52, 53, 54, 55]. Fuzzy logic has several unique features that make it a particularly good choice for many control problems:

i) It is inherently robust, since it does not require precise, noise-free inputs and can, thus, be fault-tolerant if a feedback sensor quits or is destroyed. The output control is a smooth control function despite a wide range of input variations.

ii) Since a fuzzy logic controller processes user-de?ned rules governing the target control system, it can be modi?ed and tweaked easily to improve or drastically alter system performance. New sensors can easily be incorporated into the system simply by generating appropriate governing rules.

iii) Fuzzy logic is not limited to a few feedback inputs and one or two control outputs, nor is it necessary to measure or compute rate-of-change of parameters. It is sufficient with any sensor data to provide some indication of a system’s actions and reactions. This allows the sensors to be inexpensive and imprecise thus keeping overall system cost and complexity low.

iv) Because of the rule-based operation, any reasonable number of inputs can be processed (1–8 or more) and numerous outputs (1–4 or more) generated, although de?ning a rule-base quickly becomes complex if too many inputs and outputs are chosen for a single implementation, since rules de?ning their interrelations must be de?ned, too. Then, it would be better to break the control system into smaller chunks and use several smaller fuzzy logic controllers distributed on the system, each one with more limited responsibilities.

v) Fuzzy logic can control nonlinear systems that would be difficult or impossible to model mathematically. This opens doors for control systems that would normally be deemed unfeasible for automation. In summery, fuzzy logic was conceived as a better method for sorting and handling data, and has proven to be an excellent choice for many control system applications, since it mimics human control logic. It can be built into anything from small, hand-held products to large computerized process control systems. It uses an imprecise but very descriptive language to deal with input data more like a human operator. It is very robust and forgiving of operator and data input, and often works when ?rst implemented with little or no tuning.