Abstract

The control of nonlinear systems presents a particularly challenging problem for engineers since the dynamics of such systems is inherently complex. The principle of superposition does not hold, and the dynamic response is generally initial condition specific. In 1978, the ASME’s Dynamic Systems and Control Division had published a monograph entitled Nonlinear System Analysis and Synthesis: Vol. 1 - Fundamental Principles (Edited by J. Karl Hedrick and Henry M. Paynter), which consisted of five chapters. The titles and authors of the first four chapters, respectively, were Some Fundamental Principles of Nonlinear Systems by Andrew U. Meyer; Stability of Nonlinear Systems by Kumapati S. Narendra; Nonlinear System Response: Classical Techniques for Unforced Response by Henry M. Paynter; and Nonlinear System Response: Quasi-Linearization Methods by J. Karl Hedrick. The author of the present paper has had a long standing interest in the controller synthesis research [see, for example, References 01–08]. He was also the contributor of the fifth and final chapter entitled Nonlinear Controller Synthesis, in that monograph. A number of innovative approaches have been developed for controller synthesis since the publication of the ASME monograph, particularly under the sponsorship of National Science Foundation’s Dynamic Systems and Control Program. This paper traces some of the recent developments in the area of nonlinear control system synthesis. These developments are illustrated with a few specific examples of techniques advanced during the course of research sponsored by NSF.

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