Integration of fuzzy logic and chaos theory chen guanrong li zhong
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This approach ensures that the control action remains realistic in its characteristics such as amplitude and frequency. In this work, we announce an eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities. . Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. Nowadays the new theories of soft computing are used for these purposes. Our approach is given by developing gradually the physical ideas — by starting with simple situations and going on towards the more and more complicated situations.

This volume also summarizes such trends in an industrial context. This book reviews the burgeoning industrial applications of fuzzy theory. Sliding mode control is an important method used to solve various problems in control systems engineering. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. The conditions for designing a discrete-time output regulator are given in this paper. Finding the intrinsic relation between fuzzy logic and chaos theory is certainlyofsigni? Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative.

Scientists try to explain some phenomena in Nature that have not been explained so far. It is denoted by fK in the sequel. Chaos,ontheother hand,wasconsideredoneofthethreemonumentaldiscoveriesofthetwentieth century together with the theory of relativity and quantum mechanics. Next, we present the design of adaptive feedback controller for globally stabilizing the trajectories of the novel chaotic system with unknown parameters. Gamification for Human Factors Integration: Social, Educational, and Psychological Issues presents information and best practices for promoting positive behavior online through gamification applications in social, educational, and psychological contexts. We show that Halvorsen circulant chaotic system is dissipative and that it has an unstable equilibrium at the origin. Lorenz to have random behaviours was so unusual that it was lately named a chaotic system.

But for continuous-time ones, the chaotification approach is based on the fuzzy feedback linearization and a suitable approximate relationship between a time-delay differential equation and a discrete map. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical novel hyperchaotic thermal convection systems with unknown parameters. Consequently, f is chaotic on Λ in the sense of Devaney. We would like to find some acceptable structure model of the hydrogen as a vortex-fractal-coil structure of the proton and a vortex-fractal-ring structure of the electron. Then Λ is called a Cantor set if it is compact, totally disconnected, and perfect.

Since the Vaidyanathan hyperjerk system has two positive Lyapunov exponents, it is hyperchaotic. More specifically, this book includes a collections ofsome state-of-the-art surveys, tutorials, and application examples written by some experts working in the interdisciplinary fields overlapping fuzzy logic and chaos theory. Just like irrational and imaginary numbers, negative energy, anti-matter, etc. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. The main control results are established using Lyapunov stability theory. There are diverse forms to implement a fuzzy system depending on the desired response time, for which hardware implementations are best suited for high-speed demands.

The areas covered include automobiles, home appliances, voice recognition, medical techniques, fuzzy design, process control, space operations and mobile autonomous robots. In this research work, we describe a ten-term novel 4-D four-wing chaotic system with four quadratic nonlinearities. Li where h x can be any function on x1 , x2. Control of chaotic systems is an important research problem in chaos theory. Se trata, por lo tanto, del primer esfuerzo de investigación sistemático orientado a desentrañar la lógica de la vida -y de los sistemas artificiales que exhiben características o comportamientos propios de la vida, entendiendo la vida como un fenómeno de complejidad creciente. This book can serve as a handy reference for researchers working in the interdisciplines related, among others, to both fuzzy logic and chaos theory. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems.

Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, it follows that the novel hyperchaotic system is dissipative. The phase portraits of the eleven-term novel hyperchaotic system are depicted and the dynamic properties of the novel hyperchaotic system are discussed. For this reason, we can model the uncertainty of detecting the range of values where chaos occurs, using fuzzy set theory. Some practical applications are shown in the results. The main adaptive control results are proved using Lyapunov stability theory. Specifically, all the three aforementioned controllers are applied to a nonlinear system used in the literature and it is clearly demonstrated how the proposed controller outperforms its counterparts.

In this work, we derive a novel sliding mode control method for the complete synchronization of identical chaotic or hyperchaotic systems. Thus, it follows that every non-trivial trajectory of the novel four-wing chaotic system must have a twin trajectory. Complex behavior always occurs when the saddle set is a limit cycle. The hierarchical structure of grammar-differential evolution that is used for finding optimal structures and parameters of general controllers is described. A number of hybrid systems for solving engineering problems are presented.

Sliding mode control is an important method used to solve various problems in control systems engineering. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. The general control result derived using novel sliding mode control method is proved using Lyapunov stability theory. The high value of theKaplan-Yorke dimension indicates the complexity of the novel conservative jerk chaotic system. The proposed approach guarantees that the estimation errors and external disturbances cannot affect the stability of the control system. The contributors are mostly industrial engineers or research experts in the field. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev's periodic table, which is not in contradiction to the known laws of nature.