Model Reduction of Large-Scale Dynamical Systems

A. Antoulas1, D. Sorensen2, K.A. Gallivan3, P. Van Dooren4, A. Grama5, C. Hoffmann5, and A. Sameh5

1Department of Electrical Engineering, Rice University, Houston, TX

2Department of Computational and Applied Math, Rice University, Houston, TX

3School of Computational Science, and Information Technology, Florida State University, Tallahassee, FL

4Department of Mathematical Engineering, Catholic University of Louvain, Louvain-la-Neuve, BELGIUM

5Department of Computer Sciences, Purdue University, W. Lafayette, IN

Abstract. Simulation and control are two critical elements of Dynamic Data-Driven Application Systems (DDDAS). Simulation of dynamical systems such as weather phenomena, when augmented with real-time data, can yield precise forecasts. In other applications such as structural control, the presence of real-time data relating to system state can enable robust active control. In each case, there is an ever increasing need for improved accuracy, which leads to models of higher complexity. The basic motivation for system approximation is the need, in many instances, for a simplified model of a dynamical system, which captures the main features of the original complex model. This need arises from limited computational capability, accuracy of measured data, and storage capacity. The simplified model may then be used in place of the original complex model, either for simulation and prediction, or active control. As sensor networks and embedded processors proliferate our environment, technologies for such approximations and real-time control emerge as the next major technical challenge. This paper outlines the state of the art and outstanding challenges in the development of efficient and robust methods for producing reduced order models of large state-space systems.

LNCS 3038, pp. 740-747.

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