Neural network adaptive robust control of nonlinear systems: Theory and applications

JianQin Gong, Purdue University

Abstract

The ever increasingly tight control performance requirement of modern mechanical systems often forces control engineers to look beyond traditional linear control theory for nonlinear controllers that can handle system nonlinearities directly. However, the various forms of nonlinearities in physical systems makes it difficult to have a unified framework in designing performance oriented nonlinear controllers. The situation is made even worse when precise description of nonlinearities that can be used to capture certain physical phenomena may not be known. The universal approximation capability of neural network (NN) makes it possible to design nonlinear controller in a unified framework. However, significant theoretical issues remain unsolved. These issues include the robustness of NN weight tuning rules to various modeling errors such as the external disturbances and the unavoidable functional approximation error of any implementable finite dimensional neural networks. Furthermore, the theoretically guaranteed control performance of existing NN based controllers are normally unknown, especially during the training period of neural networks. In this thesis, a neural network adaptive robust control (NNARC) strategy is proposed, which exploits NNs as on-line approximators for all unknown repeatable nonlinearities in system, uses projection mapping to achieve a controlled learning, and takes advantages of robust control to counteract approximation error. In general, NNARC can guarantee the transient performance and final tracking accuracy of closed-loop system. At the same time, when all nonlinearities are within the approximation range of neural networks, asymptotic tracking is also possible. Furthermore, when condition of persistent excitation is satisfied, the estimates of NN weights can converge to their ideal values, which achieves the learning goal of NN. Based on the essential philosophy of NNARC, a variety of NNARC algorithms are developed for different systems under different situations in this thesis. Furthermore, in order to verify their performance in reality, all of the proposed NNARC algorithms are then applied to the control of a linear motor drive system to achieve its potential of high precision. The experimental results demonstrate that, under different situations, NNARCs can not only achieve the high precision tracking performance, but also approximate unknown nonlinearities very well. It indicates that the experimental results are in accordance with the theoretical expectations.

Degree

Ph.D.

Advisors

Yao, Purdue University.

Subject Area

Mechanical engineering

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