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Unformatted text preview: Trends in Nonlinear Control Alessandro Astolfi Dragan Nesic Andrew R. Teel I. INTRODUCTION The report on an IEEE Control Systems Society Workshop held at the University of Santa Clara in 1986 reads Techniques for the control of systems described by nonlinear mathematical models are difficult, but a major breakthrough occurred during the past decade with the development of techniques which solve such control problems as disturbance decoupling, input-output de- coupling, and feedback linearization .... Since then, nonlinear control theory (and its applications) has undergone substantial developments and become one of the most active and important areas of research in the control systems community. There are several introductory and advanced textbooks devoted to nonlinear control theory, see e.g., , , , , , , , , . In turn, nonlinear control has been integrated into the stan- dard graduate curricula in engineering and applied mathemat- ics. In addition, nonlinear control theory is at the basis of the successful development and initiation of several research directions: it plays a fundamental role in the development of systems biology, in the understanding of complex commu- nication systems, power systems and cooperative systems, in the study of event driven and agent based systems, and in the development of an ever increasing number of industrial applications. Nevertheless, we maintain that the conclusion of the 1986 Workshop that techniques for the control of systems described by nonlinear mathematical models are difficult is still accurate, although we may argue on the meaning of the word difficult. Nonlinear control theory embraces a large number of research areas, which use diverse tools and methods, each well-suited for specific problems. It is therefore extremely difficult to give a tutorial presentation which represent the joint effort of the international research community, and one has to follow personal inclinations. We have therefore de- cided to emphasize three research directions that (we believe) are important, both from a methodological perspective and from the applications point of view. As a consequence we A. Astolfi is with the Department of Electrical and Electronic En- gineering, Imperial College London, SW7 2AZ, London, UK and with Dipartimento di Informatica, Sistemi e Produzione, Universita di Roma Tor Vergata, 00133 Roma, Italy. E-mail: email@example.com . D. Nesic is with The Department of Electrical and Electron- ics, The University of Melbourne, Parkville, VIC 3010. E-mail: firstname.lastname@example.org . A.R. Teel is with the Department of Electrical and Computer Engi- neering, University of California Santa Barbara, CA 93106-9560. E-mail: email@example.com ....
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- Spring '09