Li / Chen / (Eds.) Integration of Fuzzy Logic and Chaos Theory

1. Auflage 2008
ISBN: 978-3-540-32502-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 187, 641 Seiten, eBook

Reihe: Studies in Fuzziness and Soft Computing

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot? A. Zadeh were so c- fusing that they were called fuzzy set theory and fuzzy logic; a deterministic system found by E. N. Lorenz to have random behaviours was so unusual that it was lately named a chaotic system. Just like irrational and imaginary numbers, negative energy, anti-matter, etc., fuzzy logic and chaos were gr- ually and eventually accepted by many, if not all, scientists and engineers as fundamental concepts, theories, as well as technologies. In particular, fuzzy systems technology has achieved its maturity with widespread applications in many industrial, commercial, and technical ?elds, ranging from control, automation, and arti?cial intelligence to image/signal processing,patternrecognition,andelectroniccommerce.Chaos,ontheother hand,wasconsideredoneofthethreemonumentaldiscoveriesofthetwentieth century together with the theory of relativity and quantum mechanics. As a very special nonlinear dynamical phenomenon, chaos has reached its current outstanding status from being merely a scienti?c curiosity in the mid-1960s to an applicable technology in the late 1990s. Finding the intrinsic relation between fuzzy logic and chaos theory is certainlyofsigni?cantinterestandofpotentialimportance.Thepast20years have indeed witnessed some serious explorations of the interactions between fuzzylogicandchaostheory,leadingtosuchresearchtopicsasfuzzymodeling of chaotic systems using Takagi–Sugeno models, linguistic descriptions of chaotic systems, fuzzy control of chaos, and a combination of fuzzy control technology and chaos theory for various engineering practices.

Zielgruppe

Research

Autoren/Hrsg.

Li, Zhong

Chen, Guanrong

(Eds.), China

Inhaltsverzeichnis

Beyond the Li-Yorke Definition of Chaos.- Chaotic Dynamics with Fuzzy Systems.- Fuzzy Modeling and Control of Chaotic Systems.- Fuzzy Model Identification Using a Hybrid mGA Scheme with Application to Chaotic System Modeling.- Fuzzy Control of Chaos.- Chaos Control Using Fuzzy Controllers (Mamdani Model).- Digital Fuzzy Set-Point Regulating Chaotic Systems: Intelligent Digital Redesign Approach.- Anticontrol of Chaos for Takagi-Sugeno Fuzzy Systems.- Chaotification of the Fuzzy Hyperbolic Model.- Fuzzy Chaos Synchronization via Sampled Driving Signals.- Bifurcation Phenomena in Elementary Takagi-Sugeno Fuzzy Systems.- Self-Reference, Chaos, and Fuzzy Logic.- Chaotic Behavior in Recurrent Takagi-Sugeno Models.- Theory of Fuzzy Chaos for the Simulation and Control of Nonlinear Dynamical Systems.- Complex Fuzzy Systems and Their Collective Behavior.- Real-Time Identification and Forecasting of Chaotic Time Series Using Hybrid Systems of Computational Intelligence.- Fuzzy-Chaos Hybrid Controllers for Nonlinear Dynamic Systems.- Fuzzy Model Based Chaotic Cryptosystems.- Evolution of Complexity.- Problem Solving via Fuzziness-Based Coding of Continuous Constraints Yielding Synergetic and Chaos-Dependent Origination Structures.- Some Applications of Fuzzy Dynamic Models with Chaotic Properties.

Leseproben

Chaos Control Using Fuzzy Controllers (Mamdani Model) (p. 127)

Ahmad M. Harb and Issam Al-Smadi

Abstract.

Controlling a strange attractor, or say, a chaotic attractor, is introduced in this chapter. Because of the importance to control the undesirable behavior in systems, researchers are investigating the use of linear and nonlinear controllers either to get rid of such oscillations (in power systems) or to match two chaotic systems (in secure communications).

The idea of using the fuzzy logic concept for controlling chaotic behavior is presented. There are two good reasons for using the fuzzy control: .rst, mathematical model is not required for the process, and second, the nonlinear controller can be developed empirically, without complicated mathematics. The two systems are well-known models, so the first reason is not a big deal, but we can take advantage from the second reason.
1 Introduction

Modern nonlinear theories, such as bifurcation and chaos, have been widely used in many fields. Many researchers have used such theories to investigate and analyze the stability problem. Abed and Varaiya [1], Dobson et al. [2], and Harb et al. [3] used the bifurcation theory to analyze the stability of voltage collapse and SSR phenomena in electrical power systems. Endo and Chua [4] and Harb and Harb [5] analyzed the stability of phase-looked loop (PLL) in communication systems.

Nayfeh and Balachandran [6] and Harb et al. [7] analyzed the stability of Dufing oscillator in mechanical systems. Recently, research has been devoted toword the bifurcation and chaos control of such mentioned systems. The main goal of bifurcation and chaos control is stabilizing bifurcation branches, changing the type of bifurcation from subcritical to supercritical Hopf bifurcation, and delaying the bifurcations. Abed et al. [8–10] used state feedback nonlinear controllers to change the type of the Hopf bifurcation and to suppress the amplitude of the limit cycles at the vicinity of the Hopf bifurcation points.

Ikhouane and Krstic [11], Harb et al. [12, 13], and Zaher et al. [14–17] used recursive backstepping algorithms to design nonlinear controllers to stabilize systems of chaotic behavior. Fuzzy set theory has been used successfully in virtually all technical fields, including modeling, control, and signal/image processing. Fuzzy control is a rule-base system that is based on fuzzy logic. Since fuzzy is described as computing with words rather than numbers, then fuzzy control can be described as control with sentences rather than equations.

In 1974, Professor Mamdani was the first to develop the concept of the fuzzy controller. Driankov et al. [18] and Calvo and Cartwright [19] introduced the idea of fuzzy in chaos control. Tang et al. [20], Mann et al. [21], Hu et al. [22], and Gradjevac [23] used the PID fuzzy controller, while Hsu and Cheng [24] and Toliyat et al. [25] designed a fuzzy controller to enhance power system stability.