Continuous Attractors And Fuzzy Control Of Recurrent Neural Networks

Brain is the most complex, perfect and efficient information processing mechanism. People study the structure and mechanism of brain with deep interest. Intelligence is the ability to observe, learn, understand and realize. It is the most miraculous and powerful ability in the world. Intelligent behavior is based on the activity of the brain's neurons and is the result of the dynamics of neural networks. Artificial neural networks are proposed to simulate the biologic neural network. The recurrent neural network exhibiting some rich and colorful dynamical behaviors is one part of artificial neural networks. Due to their important applications in pattern recognition, image processing, computer science as well as automatic control, the dynamical issues of recurrent neural networks have attracted wide attention in recent years.This dissertation is to study two kinds of dynamics of recurrent neural network, continuous attractor and fuzzy control. It is composed of two parts, the first part mainly focuses on the continuous attractors neural networks. A lot of problems are still unsolved in this field. For example, there are no accurate definition of continuous attractors, we lack mathematics tools to study continuous attractors and how to define the attraction of the continuous attractors is complicated etc. The main contents are as follows:(1) The definition of continuous attractors is proposed. Using the eigenvalues and eigenvectors of the connection matrix, conditions are derived to guarantee the existence of the continuous attractors. Moreover, explicit representations of the continuous attractors are obtained for the first time. The continuous attractors are actually the result of the neural networks.(2) Some high dimensional continuous attractors of recurrent neural networks are investigated. There are infinite equilibria in the continuous attractors neural networks and they maybe form one dimensional curves or high dimensional manifolds. So far, continuous attractors of most studied models are one dimensional and called line attractors. In this work, high dimensional continuous attractors are builded for the first time. (3) The continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons are studied. It shows that a Lotka-Volterra recurrent neural network can possess multiple continuous attractors if the excitatory connections and the external inputs are in Gussian-like shape. Moreover, both stable and unstable continuous attractors can coexist in one network.In the second part, fuzzy controls of some recurrent neural networks are studied. Using Takagi-Sugeno (T-S) methods we can build more perfect intelligent control system. Moreover, delays take great impact to the dynamics of neural networks, so the study of delayed neural network is more important. This part mainly focuses on the dynamics of delayed T-S fuzzy systems. The main contributions of this part are as follows:(1) The global exponential stability analysis for one class of T-S fuzzy systems with uncertain bounded delays has been studied. Some novel and easily verified sufficient conditions for global exponential stability of free delayed fuzzy control systems are established via constructing an appropriate Lyapunov function. Moreover, some criteria for feedback fuzzy controller designing are given. We believe that all of the results obtained can be extended to the fuzzy systems with multiple time delays or with time-varying delays just by using another Lyapunov function.(2) The periodicity of a class of nonlinear fuzzy systems with time delays has been studied by using T-S methods. Some conditions to guarantee the existence of stable periodic solutions have been obtained. These conditions are represented by the coefficients of the local systems and quite easily to be checked.(3) Adaptive control for a class of T-S fuzzy systems is studied. Using T-S methods and IF-THEN rules, a global fuzzy nonlinear system can be represented by connecting several local systems. A feedback controller has been proposed and neural networks are used to approximate the controller so that the output of the global systems can follow the desired continuous trajectory.In conclusion, the study of this dissertation maybe will promote the investigation of intelligence.