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Efficient numerical solution of the LQR-problem for the heat equation

  1. Jens Saak,
  2. Peter Benner

Article first published online: 27 DEC 2004

DOI: 10.1002/pamm.200410305

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PAMM

PAMM

Volume 4, Issue 1, pages 648–649, December 2004

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How to Cite

Saak, J. and Benner, P. (2004), Efficient numerical solution of the LQR-problem for the heat equation. Proc. Appl. Math. Mech., 4: 648–649. doi: 10.1002/pamm.200410305

Author Information

  1. Fakultät für Mathematik, Technische Universität Chemnitz

Publication History

  1. Issue published online: 27 DEC 2004
  2. Article first published online: 27 DEC 2004

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Abstract

We discuss how the theory developed by Banks and Kunisch can be applied to a modified version of a controlled heat transfer model introduced by Tröltzsch and Unger. In the numerical implementation we use ALBERT(A) to establish the required FEM–semidiscretisation in space. The resulting algebraic Riccati equation (ARE) is of large dimension (n > 1000). It is shown how the LyaPack software package can be used to compute the optimal feedback without solving the ARE directly. In the closing section we present numerical results comparing different implementational approaches and cost functions. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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