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Chaotification of the Fuzzy Hyperbolic Model

Part of the Control Engineering book series (CONTRENGIN)

Abstract

As an intersection of chaos theory and control theory, chaos control has attracted more and more attention since the seminal work by Ott, et al. [15]. In the past decade, many researchers have studied control methods with the purpose of either reducing “bad” chaos or introducing “good” chaos [1]. Due to its great potential in nontraditional applications such as those found in the fields of physical, chemical mechanical electrical, optical, and particularly, biological and medical systems [2, 17, 26], making a nonchaotic system chaotic or maintaining existing chaos, known as “chaotification” or “anticontrol”, has attracted increasing attention in recent years. The process of chaos control is now understood as a transition from chaos to order and sometimes from order to chaos, depending on the purposes of different applications. Studies have shown that discrete maps can be chaotified in the sense of Devaney or Li-York by a state feedback controller with a control sequence of uniformly bounded gain designed to make all Lyapunov exponents of the controlled system strictly positive or arbitrarily assigned [3, 4, 20, 21, 22, 23]. Even though there are also some research works showing that certain continuous stable systems can be chaotified [12, 16, 19, 24, 25, 27, 29], how to chaotify unlinearizable nonlinear systems as well as how to make non-chaotic systems produce expected chaotic states, are still open problems.

Keywords

Lyapunov Exponent Chaotic Attractor State Trajectory Impulsive Control Chaos Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Birkhäuser Boston 2006

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