BODE LECTURER

Alberto Isidori was born in Rapallo, Italy, in 1942. His research interests are primarily focused on mathematical control theory and control engineering. He graduated in electrical engineering from the University of Rome in 1965. Since 1975, he has been Professor of Automatic Control at this University. Since 1989, he is also affiliated with the Department of Systems Science and Mathematics at Washington University in St. Louis. He has held visiting positions at various academic/research institutions which include the University of Illinois at Urbana-Champaign, the University of California at Berkeley, the ETH in Zuerich and the NASA-Langley research center. He is the author of several books, including "Nonlinear Control Systems") Springer Verlag), 1985, 1989 and 1995; "Nonlinear Control Systems II" (Springer Verlag), 1999. He is author of more than 80 articles in archival journals, of 16 book chapters and more than 100 papers on refereed conference proceedings, for a large part on the subject of nonlinear feedback design. He is also editor/co-editor of 16 volumes of Conference proceedings.

He received the G. S. Axelby Outstanding Paper Award from the Control Systems Society of IEEE in 1981 and in 1990. He also received from Automatica the Best Paper Award in 1991. In 1987 he was elected Fellow of the IEEE "for fundamental contributions to nonlinear control theory." In 1996, at the opening of 13th IFAC World Congress in San Francisco, Dr. Isidori received the "Georgio Quazza Medal" for "pioneering and fundamental contributions to the theory of nonlinear feedback control." In 2000 he was awarded the first "Ktesibios Award" from the Mediterranean Control Association.

He has organized or co-organized several international Conferences on the subject feedback design for nonlinear systems. In particular, he was the initiator of a permanent series of IFAC Symposia on this topic. From 1993 to 1996 he served in the Council of IFAC. From 1995 to 1997 he was President of the European Community Control Association.

BODE LECTURE: Finesse et Géométrie

In the first one [the esprit de géométrie], principles are tangible but far form common use, so that the mind with difficulty turns to them, and this for lack of habit; but as soon as the mind has turned a bit towards them, these principle appear in all their evidence. They are so certain that one can hardly mistakenly use them. On the contrary, in the esprit de finesse, principles are of common use and clear to the eyes of everybody. There is no need of turning the mind, but just to have a good sight: in fact, these principles are so subtle and so many that it is almost impossible not to miss one of them, (Pascal, Pensées, 1670).

In the last three decades, geometry has proven to be the right tool in understanding "do"s and "don't"s in feedback design, linear and nonlinear. Perhaps, the single most important reason for widespread use of geometric ideas in feedback design is the ability, of geometry, to provide intrinsic characterizations of so many "feedback invariants." This is particularly manifest in the case of feedback design for nonlinear systems, where the paradigm of seeing a system as a "linear fractional transformation" no longer makes sense, and where the methods of differential geometry have proven to be the most effective tool for analysis. Nevertheless, geometry alone is not enough to completely answer a feedback design problem, as in the last instance a less systematic, but more intuitive and comprehensive, approach always becomes necessary to settle those capital issues such as stability and robustness. Thus, "geometers" and "fine spirits" are both indispensable for feedback design. Unfortunately however, as Pascal himself observed, "it seldom occurs that geometers are fine spirits and that fine spirits are geometers."

In this lecture, it is shown how rigorous and systematic esprit de géométrie is instrumental in understanding some intrinsic features of a good controller and, eventually, to bring a sensible amount of certainty into the design of a feedback law. As a prototypical example, the problem of tracking/rejecting uncertain exogenous inputs in the presence of plant parameter uncertainties is considered. In such a problem, only the esprit de géométrie can tell what the intrinsic features of a good controller have to be. These features uniquely determine the structure of the controller, essentially up to the design of a (robust) stabilizer. It is here that the esprit de finesse enters the stage and provides a variety of options for a successful completion of the design. An application to (uncertain) path following for an underactuated air vehicle is described.