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Upper and Lower Bounds in Multi-Objective Control

We revisit the multi-objective control problems with closed-loop performance specifications that admit LMI representations, such as in H2/H-infinity-control. In a typical approach, such a problem is transformed with the Youla parameterization to an infinite dimensional optimization problem which is approximately solved by restricting the search to a sequence of finite dimensional subspaces. In all algorithms proposed so far, the resulting semi-definite programming problems suffer from a dramatic inflation of size if improving the approximation accuracy by increasing the subspace dimension. In this talk we present a novel technique that allows to avoid this inflation in order to render these techniques amenable to more realistically sized systems as they appear in practical applications. For general scenarios, it is up to now only possible to compute a sequence of upper bounds that converges to the optimal value. As a second topic of this talk we will reveal how one can as well determine a converging sequence of lower bounds by solving suitable semi-definite programs what leads to stopping criteria for guaranteeing a certain approximation quality.

Type of Seminar:
Public Seminar
Dr. C.W. Scherer
Mechanical Engineering Systems and Control Group Delft University of Technology, The Netherlands
Sep 22, 1999   14:15

ETH-Zentrum, ETL K 25, Physikstrasse 3, 8006 Zurich
Contact Person:

Ms Danielle Couson
No downloadable files available.
Biographical Sketch:
Carsten Scherer received the diploma degree and the Ph.D. degree in mathematics from the University of Würzburg (Germany) in 1987 and 1991 respectively. In 1989, Dr. Scherer spent six months as a visiting scientist at the Mathematics Institute of the University of Groningen (The Netherlands). In 1992, he was awarded a grant from the Deutsche Forschungsgemeinschaft (DFG) for six months of post doctoral research at the University of Michigan (Ann Arbor) and at Washington University (St. Louis) respectively. In 1993 he joined the Mechanical Engineering Systems and Control Group at Delft University of Technology (The Netherlands) where he currently holds a position as an associate professor (universitair hoofddocent). His main research interests cover various topics in applying optimization techniques for developing new advanced controller design algorithms and their application to mechatronics and aerospace systems. Currently, Dr. Scherer spends a three months sabbatical at the Automatic Control Laboratory at ETH Zurich.