Arjan J. van der Schaft (Univ. of Twente, The Netherlands),
Romeo Ortega (SUPELEC, CNRS, France), Pierre Rouchon (Ecole des Mines de
Paris, France), Georges BASTIN (CESAME, Belgium), and Stefano Stramigioli
(Delft University of Technology, The Netherlands)
Nonlinear systems and control theory has witnessed tremendous developments over the last three decades. Especially the introduction of geometric tools like Lie brackets of vector fields on manifolds has greatly advanced the theory, and has enabled the proper generalization of many fundamental concepts known for linear control systems to the nonlinear world. While the emphasis in the eighties has been primarily on the structural analysis of smooth nonlinear dynamical control systems, in the nineties this has been combined with analytic techniques for stability, stabilization and robust control, leading e.g. to backstepping techniques and nonlinear H¥ control. Moreover, in the last decade the theory of passive systems, and its implications for regulation and tracking, has undergone a remarkable revival. This last development was also spurred by work in robotics on the possibilities of shaping by feedback the physical energy in such a way that it can be used as a suitable Lyapunov function for the control purpose at hand. This has led to what is sometimes called passivity-based control. Many other important developments have taken place, and much attention has been paid to special subclasses of systems like mechanical systems with nonholonomic constraints.
All this has resulted in a very lively research in nonlinear control, with many actual and potential applications. The aim of the course "Physics in Control" is to stress the importance of physical modeling for nonlinear control. In some sense, this is common knowledge for everyday control engineering, but a general theoretical framework for modeling is also of utmost importance for the development of nonlinear control theory. Indeed, although in principle the same applies to linear control systems, in the latter case the relative ease of general linear control techniques may obviate the need for a representation of the system which makes explicit the physical characteristics of the system. On the other hand, the class of general nonlinear control systems is so overwhelmingly rich, that it cannot be expected that a single theory will cover the whole area, thus necessitating the exploitation of the inherent physical structure of many nonlinear control systems. In the course some of the recent developments in systems and control theory of physical systems will be highlighted. This will include the Hamiltonian geometrization of network models of physical systems, and its implications for impedance control and passivity-based control. Apart from the energy balance which is so prominent in Hamiltonian models and the theory of passive nonlinear systems, other physical balance relations such as mass balance can play a crucial role. Also the study of symmetries and its consequences for control substantialy adds to this framework. Application areas of these approaches range from mechanical systems, robot manipulators, induction motors, power systems to (bio-) chemical processes.