Graduate Thesis Or Dissertation

Neural network control of nonlinear discrete time systems

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  • The main focus of this work is on the problem of existence of nonlinear optimal controllers realizable by artificial neural networks. Theoretical justification, currently available for control applications of neural networks, is rather limited. For example, it is unclear which neural architectures are capable of performing which control tasks. This work addresses applicability of neural networks to the synthesis of approximately optimal state feedback. Discrete-time setting is considered, which brings extra regularity into the problem and simplifies mathematical analysis. Two classes of optimal control problems are studied: time-optimal control and optimal control with summable quality index. After appropriate relaxation of the optimization problem, the existence of a suboptimal feedback mapping is demonstrated in both cases. It is shown that such a feedback may be realized by a multilayered network with discontinuous neuron activation functions. For continuous networks, similar results are obtained, with the existence of suboptimal feedback demonstrated, except for a set of initial states of an arbitrarily small measure. The theory developed here provides basis for an attractive approach of the synthesis of near-optimal feedback using neural networks trained on optimal trajectories generated in open loop. Potential advantages of control based on neural networks are illustrated on application to stabilization of interconnected power systems. A nearly time-optimal controller is designed for a single-machine system using neural networks. The obtained controller is then utilized as an element of a hierarchical control architecture used for stabilization of a multimachine power transmission system. This example demonstrates applicability of neural control to complicated, nonlinear dynamic systems.
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