Structure preservation: a challenge in computational control

  • Authors:

  • Peter Benner;Daniel Kressner;Volker Mehrmann

  • Affiliations:

  • Institut für Mathematik MA 4-5, TU Berlin, Str. des 17, Juni 136, D-10623 Berlin, Germany;Institut für Mathematik MA 4-5, TU Berlin, Str. des 17, Juni 136, D-10623 Berlin, Germany;Institut für Mathematik MA 4-5, TU Berlin, Str. des 17, Juni 136, D-10623 Berlin, Germany

  • Venue:
  • Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
  • Year:
  • 2003

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Abstract

Current and future directions in the development of numerical methods and numerical software for control problems are discussed. Major challenges include the demand for higher accuracy, robustness of the method with respect to uncertainties in the data or the model, and the need for methods to solve large scale problems. To address these demands it is essential to preserve any underlying physical structure of the problem. At the same time, to obtain the required accuracy it is necessary to avoid all inversions or unnecessary matrix products. We will demonstrate how these demands can be met to a great extent for some important tasks in control, the linear-quadratic optimal control problem for first and second order systems as well as stability radius and H∞ norm computations.