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Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition

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Abstract

Proper orthogonal decomposition (POD) is a method to derive reduced-order models for dynamical systems. In this paper, POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation. The relative simplicity of the equation allows comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system. For closed-loop control, suboptimal state feedback strategies are presented.

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Authors and Affiliations

  1. Institut für Mathematik, Karl-Franzens-Universität Graz, Graz, Austria

    K. Kunisch (Professor)

  2. Institut für Mathematik, Karl-Franzens-Universität Graz, Graz, Austria

    S. Volkwein (Assistant Professor)

Authors
  1. K. Kunisch
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  2. S. Volkwein
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Kunisch, K., Volkwein, S. Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition. Journal of Optimization Theory and Applications 102, 345–371 (1999). https://doi.org/10.1023/A:1021732508059

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  • DOI: https://doi.org/10.1023/A:1021732508059

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