The field of control is inherently interdisciplinary in nature and extends from design, development and production on the one hand to mathematics on the other. The objective of control is to influence the behavior of dynamical systems. Achieving fast and accurate control under different environmental conditions, even while assuring stability and robustness, is the aim of all control systems design. The best developed part of control theory deals with linear systems, and most of the controllers used in modern industry are based on linear control principles. When some of the parameters of the system are unknown, we have an adaptive control problem. The complexity of the problem is substantially greater when the plant characteristics are known but distinctly nonlinear, and becomes truly formidable when some of its parameters/functions are unknown or vary with time. Very few methods currently exist for controlling such systems. However, as applications in industry are becoming more complex and the frontiers of technology are being extended, such problems are being encountered with increasing frequency. This is the case both in well established areas such as process control and aircraft control, as well as new areas such as space technology, robotics, and manufacturing. New methods for addressing such problems using neural networks will be studied in this project. This project consists of four parts. The first part deals with some of the important questions related to neural network based identification and control that require further investigation. In the second part, the problem of control based on pattern recognition, and the use of neural networks in optimal control, are studied. The third part re-examines the question of stability of neural network based control systems. The PI believes that the first three parts are essential for a better understanding of the difficulties encountered in nonlinear adaptive control, and that they will set the stage for the fourth and final part, which contains the main thrust of the work. Here, a detailed study will conducted of the problem of controlling both linear and nonlinear dynamical systems using multiple models, when time variations and external perturbations are present.
