Adaptive Identification and Control of Dynamical Systems Using Neural Networks

Yale University, New Haven CT

Investigators

Abstract

0113239 Narendra The mathematical difficulties encountered in designing controllers for dynamical systems can be broadly classified under four headings: (i) uncertainty (ii) nonlinearity (iii) complexity, and (iv) time-variations. Adaptive control is the discipline which deals with uncertainty in systems, and the adaptive control of linear systems is currently well understood. The problem of control becomes substantially more complex when the plant characteristics are known but nonlinear, and becomes truly formidable when they are unknown and/or vary with time. All four classes of problems are encountered when neural networks are used to control nonlinear plants. During the past ten years considerable progress has been made in understanding the problems that arise in neurocontrol [1]- [18]. Mathematical modeling, system identification, and synthesis of controllers to track desired output signals have all been extensively studied. The effect of different classes of disturbances have also been investigated, and the methods developed have been applied to a wide class of practical problems. In spite of this, many important questions remain unanswered, and the design of neural controllers remains in many cases more an art than a science. The proposal addresses three fundamental and closely related questions in the adaptive control of nonlinear dynamical systems. The first concerns questions of stability and convergence of neural network based control and deals with both the structure of the controllers and the tools used for proving stability. The second question deals with the important problem of generating optimal control inputs for general classes of nonlinear systems. Such problems are arising with increasing frequency in both well established areas such as process control and aircraft control, as well as new areas such as robotics and space technology. Finally, the third problem deals with the use of multiple models for controlling efficiently nonlinear systems in rapidly varying environments. In all three cases the principal questions are stated, the mathematical difficulties are discussed in detail, and potentially fruitful avenues for research are proposed. It is the opinion of the PI that, in the present state of development of neurocontrol, the three parts of the proposal represent three closely related and important aspects of nonlinear adaptive control using neural networks.