Entropy optimization for fuzzy modeling and adaptive learning control of nonlinear dynamics.

摘要

Sensitive dependence of a dynamical system's temporal evolution to perturbations of the initial conditions is ubiquitous in nonlinear dynamics. Two identical chaotic systems starting at nearly the same point follow trajectories that divert rapidly from each other and become quickly uncorrelated. In this dissertation, a framework for fuzzy modeling, adaptive learning control and synchronization of nonlinear dynamics is proposed. This framework is based on information theoretic criteria. For fuzzy model identification, we present an approach to constructing a self-organizing fuzzy identifier. The proposed identifier is built on a neuro-fuzzy system consisting of a maximum entropy self-organizing net (MESON) and a radial basis function network (RBFN). We develop the corresponding self-organizing algorithms. MESON is used for the generation of fuzzy rules as well as the construction of RBFN for fuzzy inference. We further extend the ideas of MESON and give more detailed study of adaptive control of chaotic systems. The proposed method is a neuro-fuzzy model as a globally coupled map based on entropy optimization, which combines an identified system fuzzy model and a control input update rule. The asymptotical stabilities of the proposed adaptive learning control system as well as MESON are shown in the sense of Lyapunov. The proposed adaptive control strategy can be successfully applied to the problem of synchronization of chaos. We introduce a scheme of controlling the dynamics of a deterministic system by coupling it to the dynamics of another similar system. The controlled system synchronizes its dynamics with the control signal in the periodic as well as chaotic regimes. The method can be seen also as another way of controlling the chaotic behavior of a coupled system. In the case of coupled chaotic systems, under the interaction between them their chaotic dynamics can be cooperatively self-organized. Furthermore, the complex dynamical behavior in spatially extended systems is investigated. The concept of self-organization in complex dynamical systems and the role of entropy are presented. A quantitative measure of the degree of self-organization as a function of coupling parameter is given through information measures.