The traditional control methods are based on the exact mathematical models of plants. But in many practical applications, the mathematical function describing a real-world system can be very complex and its exact form is usually unknown. Neural networks have provided new ways for this purpose, which is due to their powerful ability of information processing, especially the ability of approximating an arbitrary nonlinear mapping. So the neural networks control have become the main method of the intelligent control, which is called the third generation control. The dissertation deals deeply with neural networks structures and several important problems existed in neural networks for nonlinear dynamical system analysis and synthesis. The main research works are as follows: Various control structures using neural networks for nonlinear dynamical systems are addressed systematically. Characterization and implementation of various structures are briefly discussed. More details are given about the ability of neural networks approximating an arbitrary nonlinear mapping and various forms of identification structures using neural networks for the unknown nonlinear dynamical system. From the approximation point of view, a novel neural network structure polynomials network is developed. It overcomes difficulties of defining numbers of hidden layers and hidden units and additional calculation in feed forward neural networks. It provides a practical and valid method to realize the best approximation in discrete point sets of a continues function. The polynomials network is derived from single variable to multiple variables. The learning algorithm is given and the convergence is discussed. In order to process nonlinear dynamical system identification in this network, a linear dynamical network is added so that the polynomials network has less inputs than recurrent networks. To overcome the slow convergence and locally optimal solutions, a new improved learning algorithm is presented. Through simulation tests it is proved that the proposed algorithm can yield faster, more efficient training procedures. The state observer design for nonlinear dynamical system is a very important problem in nonlinear dynamical system synthesis. Methods on traditional observer design for nonlinear dynamical system are briefly summarized. Based on these methods, a new way is presented which combined the idea of feedback and the theory of learning adjustment. By the error between the plant output and the observer output , the state of the observer is adjusted. As a result, the difficulty of solving the nonlinear feedback function is avoided. Regulation and tracking of a dynamical system are two basic forms in control. These design methods are based on the nonlinear theory and its implementation is finished by neural networks. In state regulation, this paper considers three forms: linear feedback, feedback lin
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