Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

11 Neural Networks in Control Systems

Kumpati S. Narendra Sai-Ming Li Yale University


1. INTRODUCTION

Control theory is an interdisciplinary field elaborating on principles and models that apply to systems in general, irrespective of the specific elements involved. The past five decades have witnessed major advances in control theory made through a combination of mathematics, modeling, computation, and experimentation. During the past 10 years there has also been an explosive growth in pure and applied research related to neural networks. In this chapter we show how the concepts and methods developed in these two areas can be suitably combined for the control of complex dynamical systems.

Control theory deals with the process of influencing the behavior of a dynamical system so as to achieve a desired objective. Generally, this objective is to maintain the outputs of a system around prescribed constant values (regulation) or to follow predetermined time functions (tracking). The history of automatic control has been the constant striving toward achieving these objectives with increased speed and accuracy. The best developed part of control theory deals with linear time- invariant systems, and frequency- and time-domain methods for the analysis and synthesis of such systems are well established.

It is well known that the concept of feedback can be used to achieve increased accuracy. It is also known, however, that feedback brings in its wake the problem of stability. Because of the presence of feedback, small changes in the initial conditions of the system may be amplified and result in large deviations in its overall behavior (i.e., the system is unstable). Hence, determining conditions under which speed and accuracy can be improved without affecting stability is the main objective of all control systems. Such conditions have been developed

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