Catálogo de publicaciones - libros

In this chapter, chaotifying both discrete-time and continuous-time Takagi-Sugeno (TS) fuzzy systems is introduced. To chaotify discrete-time TS fuzzy systems, the parallel distributed compensation (PDC) method is employed to determine the structure of a fuzzy controller so as to make all Lyapunov exponents of the controlled TS fuzzy system strictly positive. But for continuous-time ones, the chaotification approach is based on fuzzy feedback linearization and a suitable approximate relationship between a time-delay differential equation and a discrete map. The time-delay feedback controller, chosen among several candidates, is a simple sinusoidal function of the delay states of the system, which can have an arbitrarily small amplitude. These anti-control approaches are all proved to be mathematically rigorous in the sense of Li and Yorke. Some examples are given to illustrate the effectiveness of the proposed anti-control methods.

This chapter introduces digital control of chaotic systems represented by TS fuzzy systems using intelligent digital redesign (IDR) techniques. The term, intelligent digital redesign, involves converting an existing analog TS fuzzymodel- based controller into an equivalent digital counterpart in the sense of state-matching. The IDR problem is viewed as a minimization problem of norm distances between nonlinearly interpolated linear operators to be matched. The main features of this method are that its constructive condition, with global rather than local state-matching for given chaotic systems, is formulated in terms of linear matrix inequalities (LMI). The stability property is preserved by the proposed IDR algorithm. A set-point regulation example of a chaotic system is demonstrated to visualize the feasibility of the developed methodology, which implies safe digital implementation of chaos control systems.

In this chapter, spatiotemporal chaos in arrays of coupled fuzzy-logic-based chaotic oscillators is observed, and the effects of network topology on synchronization through de.ning a synchronization index are investigated in the framework of complex networks.

As an application example of integrating fuzzy logic and chaos theory, a fuzzymodel-based chaotic cryptosystem is introduced in this chapter.