Model Reduction of Large-Scale Dynamical Systems

Prof. Anthanasios C. Antoulas

   Zeit: Dienstag, 23. 5. 2000, 16:00
   Ort: Hörsaal V 9.31 Pfaffenwaldring 9, Universitätsbereich Stuttgart-Vaihingen

Direct numerical simulation of dynamical systems has been a successful means for studying complex physical phenomena. However, as more detail is included, the dimensionality of such simulations may increase to unmanageable levels of storage and computational requirements. One approach to overcoming this is through model reduction. The goal is to produce a low dimensional system that has the same response characteristics as the original system with far less storage requirements and much lower evaluation time. The resulting reduced model might be used to replace the original system as a component in a larger simulation or it might be used to develop a low dimensional controller suitable for real time applications.

Currently there are two basic methodologies for model reduction. The first is based on the Singular Value Decomposition (Hankel norm/balanced methods) while the second is based on moment matching (Lanczos/Arnoldi methods). The main features are: guaranteed properties of the approximant (preservation of stability) and the existence of global error bounds, for the former, and numerical efficiency/stability for the latter. The challenge consists in devising methods which combine the features of both methodologies.

The goal of this lecture is to present an overview of existing results together with some recent advances in addressing this challenge.

Biographical Sketch:

Thanos Antoulas was born in Athens, Greece. He studied at the ETH Zürich, where he obtained the Diploma of Electrical Engineering in 1975, the Diploma of Mathematics in 1975, the Ph.D. Degree in Mathematics in 1980, and the Habilitation Degree in Mathematics in 1983. He was Professor R.E. Kalman's only Ph.D. student in Switzerland. Since 1982 he has been with the Department of Electrical and Computer Engineering, Rice University, where he is currently a Professor. He is also holding the position of lecturer in Mathematics at the ETH Zürich, since 1983.

Professor Antoulas was elected Fellow of the IEEE (Institute of Electrical and Electronics Engineers) in 1991 and was awarded the Best Paper Prize of the AIAA (American Institute of Aeronautics and Astronautics) Guidance, Navigation and Control Section, in 1992. In 1995 he was awarded a JSPS (Japan Society for the Promotion of Science) Fellowship. He has served on the Editorial Board of many journals including the IEEE Transactions on Automatic Control, SIAM Journal on Control and Optimization, and Linear Algebra and its Applications. For the past 5 years he has been serving as Editor-in-Chief of Systems and Control Letters.

He has held several visiting appointments, including those at the Australian National University, the University of Groningen, the Tokyo Institute of Technology and Kyoto University. Furthermore he has given invited presentations at numerous conferences and workshops. His research interests are in the area of modeling and control of complex dynamical systems. In order to foster interdisciplinary activity in the broad area of dynamical systems. Professor Antoulas, in collaboration with Professor Fathi Ghorbel of the Mechanical Engineering Department, founded in 1998 the Dynamical Systems Group (DSG) at Rice University.