Einladung zum Vortrag im Kolloquium Technische Kybernetik

Optimal robust feedback control of constrained linear time delay systems

Dr. Natalia Dmitruk
Institute of Mathematics
National Academy of Sciences of Belarus
Minsk, Belarus

    Zeit: Dienstag· 30. 10. 2007 · 16:00 Uhr
    Ort: IST-Seminarraum 3.241 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

In this presentation we consider linear time-delay systems under unknown but bounded disturbances and discuss how to control the system in order to steer it in finite-time to a given terminal set while minimizing a linear cost functional. Ideally, for the control problem in question one would like to construct the optimal feedback as obtained by dynamic programming. However, in practice this technique is in general computationally intractable, and simplifications of feedback synthesis methods are usually proposed. For example, the simplest way to define a suitable feedback is to solve repeatedly the open-loop optimal control problem and to apply the resulting optimal input until the next state measurement arrives. This is a so called open-loop optimal feedback. While it is easy to construct such a feedback, it results in very conservative behavior of the closed-loop due to the fact that one control is supposed to be good for all possible realizations of the disturbance. To overcome the drawbacks of dynamic programming implementation and open-loop optimal feedback control we propose an intermediate control strategy. As in open-loop optimal feedback control, we utilize the idea of repeated solution of some predictive optimal control problem. However, now in the formulation of this problem we explicitly take into account the fact that at some limited number of future sampling instants, called closing instants, the new state becomes available, system is closed and the optimal input is corrected. The resulting feedback is referred to as multiply-closed optimal feedback control. It coincides with the open-loop optimal feedback when zero closing instants are considered and with dynamic programming scheme when all sampling instants are taken into account in the predictive optimal control problem. Thus, choosing a number of closing instants we achieve a compromise between the performance of the closed-loop and the computational efforts for feedback construction. In the presentation, besides the conceptual description of multiply-closed optimal feedback control, we will discuss a suitable finite-dimensional characterization of infinite-dimensional states of time-delay systems, derive the existence result and propose a computationally attractive algorithm for feedback construction.

Biographical Information

Natalia Dmitruk graduated in Applied Mathematics from the Belarusian State University in Minsk in 1997 and received her Ph.D. degree in Mathematics at the Institute of Mathematics of the National Academy of Sciences of Belarus in 1999. Since 1997 she has held the research position at the Institute of Mathematics and since 2000 she has been assistant professor at the Belarusian State University. In 2004 she was with Institute of Calculus Application, Bari under CNR-NATO Fellowship. In 2006 and 2007 she visited IST with the research grant from DAAD. Her main research interests include optimal control theory, optimal state and measurement feedback synthesis and real-time optimization.