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

Author

Listed:
  • K. Kunisch

    (Karl-Franzens-Universität Graz)

  • S. Volkwein

    (Karl-Franzens-Universität Graz)

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.

Suggested Citation

  • K. Kunisch & S. Volkwein, 1999. "Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 345-371, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021732508059
    DOI: 10.1023/A:1021732508059
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    Cited by:

    1. Luo, Zhendong & Li, Hong & Sun, Ping & An, Jing & Navon, Ionel Michael, 2013. "A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 50-68.
    2. Saifon Chaturantabut & Danny C. Sorensen, 2010. "Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(4), pages 337-353, July.
    3. Luo, Zhendong & Jin, Shiju & Chen, Jing, 2016. "A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 396-408.
    4. A. M. Croicu & M. Y. Hussaini, 2008. "Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 501-514, December.

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