Einladung zum Vortrag im Kolloquium Technische Kybernetik
A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Control
Prof. Herbert Werner
Technische Universität Hamburg-Harburg
Zeit: Montag · 9. 5. 2005 · 14:00 Uhr
Ort: Raum 3.241 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen
A major obstacle to the widespread use of modern control techniques such as H2 or H-infinity optimal controller design is the fact that they can be applied only under restrictive assumptions. The controller must have the same order as the (generalized) plant, and there must be no constraints on the information structure of the feedback loop (such as decentralized control). Without these assumptions the synthesis problem becomes non-convex; in fact it has been shown that many such control problems of practical interest are NP-hard.
It is however interesting to observe that there is a considerable difference in complexity between analysis problems and synthesis problems: the former are often convex and easy to solve, whereas the latter are intractable. This raises the question whether it is not more efficient to use easy-to-get analysis results to guide a stochastic search for the solution, rather than to address the hard synthesis problem directly. Recently, the use of randomized search techniques for solving such non-convex problems has been proposed in the framework of statistical learning theory. This search leads to a solution that cannot be claimed to be optimal, but the probability of finding a better controller is less than a user-specified value. However, even though this approach leads to polynomial-time solutions, it turns out that for realistic problems the required computational effort is too high for practical use.
This presentation introduces an alternative approach that is based on a combination of algebraic tools from optimal control theory, and evolutionary techniques. Several benchmark problems representing "hard" control problems are used to illustrate the efficiency of the approach and to compare it with previously published solutions.
Herbert Werner received the Dipl.-Ing. degree from the Ruhr University Bochum, the MPhil degree from the University of Strathclyde, UK, and the PhD degree from the Tokyo Institute of Technology, Japan, in 1989, 1991 and 1995, respectively. From 1995-98 he was with the Control Engineering Laboratory at the Ruhr University Bochum, and from 1999-2002 with the Control Systems Centre at UMIST, UK. Since 2002 he has held the Chair of Control Engineering at the Technical University Hamburg-Harburg, Germany. His current research interests include linear systems theory, robust and gain-scheduled control systems, and modelling of uncertain or time-varying systems.