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Workshop of Prof. van der Schaft 2004

February 05th-06th 2004, Linz, Austria

Energy and Geometry in Nonlinear Control

Workshop Prof. van der Schaft n this course an introduction is given to geometric nonlinear control theory. In the first part of the course the basic concepts of nonlinear controllability and observability are treated with tools from coordinate-free analysis such as Lie brackets of vector fields. This is illustrated by simple examples from mechanical systems. Next issues around (partial) feedback linearization are addressed where we wish to transform the nonlinear control system into a linear one, in order to apply linear control techniques. Examples to tracking control will be included. Second part of the talk is concerned with a basic treatment of stability and stabilization of nonlinear control systems. Focus is on linearization and the use of Lyapunov functions. Dissipative systems are introduced, and the basic small-gain and passivity theorems are given in time-domain. In the third part of the talk we concentrate on nonlinear systems with physical structure, in particular port-Hamiltonian systems as arising from network modelling. The relation with dissipative systems are given, and control strategies based on the physical properties of the system are indicated.

References:
H. Nijmeijer, A.J. van der Schaft,
Nonlinear Dynamical Control Systems,
Springer-Verlag, New York, 1990 (4th printing 1998), p. xiii+467.

A.J. van der Schaft,
L2-Gain and Passivity Techniques in Nonlinear Control,
Lect. Notes in Control and Inf. Sciences, Vol. 218, Springer-Verlag, Berlin, 1996, p. 168, 2nd revised and enlarged edition, Springer-Verlag, London, 2000 (Springer Communications and Control Engineering series), p. xvi+249.

R. Ortega, A.J. van der Schaft, I. Mareels & B.M. Maschke:
Putting energy back in control, Control Systems Magazine, 21, pp. 18-33, 2001.


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