This dissertation presents neural network dynamical system approaches to problems in three areas of mathematical control. The areas are storage and retrieval of appropriate control actions, processing the control signal, and synthesis of a controller. The neural network dynamical system approaches are: the Spherical Classifier Neural Network (SC), the High Order Conversion Neural Network (HOCNN), and the Spherical Classifier Feedforward (SCFF) neural network controller.;The SC is an artificial neural network dynamical system for associative content addressable memory (ACAM). It is capable of storing real-valued vectors as asymptotically stable equilibria of the dynamical system. The constant attractors for the spherical classifier are prespecified unit vectors.;The HOCNN is a high order neural network for analog-to-digital (AD) conversion implemented in digital control systems. The signal conversion process is a simple example of how high order neural networks can be constructed to solve a variety of set selection and set domination problems. The model is a difference equation dynamical system. It is shown to have a single, asymptotically stable equilibrium for a given analog input. A comparison with other neural network approaches to a signal matching process is given.;The SCFF is a hybrid neural network control system consisting of a neural network dynamical system and a multi-layer neural network. The control scheme is used for on-line identification and adaptive control of nonlinear dynamical systems. The neural network dynamical system, called the spherical classifier, serves as a memory device while the weights or parameters of the multi-layer network serve as the content associated with a memory. The capability of this technique is demonstrated by building a neurocontroller for the two-link robot manipulator and the truck backer-upper.
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