Invitation to the
Peter Sagirow Distinguished Seminar Series
of the University of Stuttgart

Open Dynamical Systems and Their Origins

Prof. Jan C. Willems Department of Electrical Engineering Katholieke Universiteit Leuven Leuven Belgium

Abstract

The aim of this lecture is to sketch the historical developments of the notion of a dynamical system as it is used in mathematics, physics, and engineering.

The first line of ideas goes back to celestial mechanics. Kepler's laws, Newton's equations, and then-body problem led to the notion of a flow, as formalized by Poincaré, Birkhoff, and Smale. This is very much a theory of closed systems, meaning that the dynamics do not take into consideration external influences. Chaos theory, for example, functions in this setting.

The second line of thinking has been developed mainly in engineering. The central notion here is an input/output system. In this setting a system is viewed in terms of action and reaction, as a cause/effect relation, and it is precisely the response to external stimuli that is the central concern. The origin of these ideas can be traced back to Heaviside, the early days of circuit theory and control, and to Wiener and his Cybernetics.

Around 1960, state space models came in vogue in control theory. This led to a view of a system as a combination of a controlled state transition with a read-out map. This framework has both flows and input/output systems as special cases, and has much more expressive modeling power. Optimal control theory à la Pontryagin as initiated in the former Soviet Union was instrumental in realizing this paradigm shift, but it is especially through the work of Kalman that state space systems came to dominate system and control theory. State models are used for example in Model Predictive Control, a controller design technique which is highly successful in industrial applications.

Recently a framework has been developed, called the behavioral approach, which does not start with a partition of the external variables in inputs and outputs, and in which first principles models are viewed in terms of manifest and latent variables. The merits of this point of view will be sketched through the seminal notion of controllability and by the attempt to provide a sound formulation of the laws of thermodynamics.

About the speaker

Prof. Jan C. Willems studied engineering at the University of Ghent. After graduation in 1963, he worked towards a PhD degree in electrical engineering at the Massachusetts Institute of Technology that he obtained in 1968. He was an assistant professor there from 1968 to 1973. In 1973, he was appointed Professor of Systems and Control in the Mathematics department of the University of Groningen. He became emeritus in 2003. Since 2003, he has been a Guest Professor at the department of electrical engineering of the Katholieke Universiteit Leuven in Belgium.

Prof. Willems has been one of the greatest contributors to the field of automatic control over the past 40 years. Early in his career he made seminal contributions to the study of dissipativity that still form the basics for many modern developments. He introduced the highly fruitful concept of "almost invariance" in geometric control theory, and he is the father of the behavioral approach to systems and control. Prof. Willems received may awards and honors, including the IEEE Control System Award, he is founding editor of the Systems and Control Letters, and is a highly influential teacher as well as a gifted educator. Many of the famous control professors of today obtained their PhD under the supervision of Jan C. Willems. More details are given on http://homes.esat.kuleuven.be/~jwillems/webpage.html .

Date:	Wednesday, November 29, 2006
Time:	4 p.m.
Location:	Room V 38.04, Universitätsstraße 38, Campus Stuttgart-Vaihingen