SOME OPTIMAL CONTROL AND NON-LINEAR DYNAMIC SYSTEM DESIGN PROBLEMS

Abstract

Automatic control has played a vital role in the advancement of engineering and science. In addition to its extreme importance in space-vehicles, missile-guidance ' systems, aircraft-auto piloting systems, robotic systems and the like, it has also become an important and integral part of the modern manufacturing and industrial processes. The concept of control system optimization comprises of selection of a performance index and a design which yields the optimal control system within limits imposed by the physical constraints. Owing to increasing demand for systems of high performance, problems of optimal control have received a good deal of attention from control engineers during the past three decades. Analytic solutions of optimal control problems provide good insight into the nature of optimal structures and help in developing algorithms for analyzing practical optimal control problems. Mathematical system theory , which in the past five decades has evolved into a powerful scientific discipline of wide applicability, deals with analysis and design of dynamical systems. The best developed aspect of the -theory treats a system defined by .linear operators using well established techniques based on linear algebra, linear differential / difference equations. The design techniques for a dynamical system are closely related to their stability properties. Necessary and sufficient conditions for the stability of linear time-invariant systems have been established over the past century, IV and well-known design methods exist for linear systems. In contrast to this, the stability of nonlinear systems can be established for the most part only on a system - by - system basis. Hence it is not surprising that design procedures that simultaneously meet the requirements of stability, robustness, and good dynamical response are not easily available for large classes of such systems.