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Boundary Stabilization for a Heat-Kelvin-Voigt Unstable Interaction Model, with Control and Partial Observation Localized at the Interface Only

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Listed:
  • Irena Lasiecka

    (University of Memphis
    IBS, Polish Academy of Sciences)

  • Rasika Mahawattege

    (University of Maryland Baltimore County)

  • Roberto Triggiani

    (University of Memphis)

Abstract

A prototype model for a Fluid–Structure interaction is considered. We aim to stabilize [enhance stability of] the model by having access only to a portion of the state. Toward this goal we shall construct a compensator-based Luenberger design, with the following two goals: (1) reconstruct the original system asymptotically by tracking partial information about the full state, (2) stabilize the original unstable system by feeding an admissible control based on a system which is obtained from the compensator. The ultimate result is boundary control/stabilization of partially observed and originally unstable fluid–structure interaction with restricted information on the current state and without any knowledge of the initial condition. This prevents applicability of known methods in either open-loop or closed loop stabilization/control.

Suggested Citation

  • Irena Lasiecka & Rasika Mahawattege & Roberto Triggiani, 2024. "Boundary Stabilization for a Heat-Kelvin-Voigt Unstable Interaction Model, with Control and Partial Observation Localized at the Interface Only," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1471-1508, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02477-4
    DOI: 10.1007/s10957-024-02477-4
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    1. Schumacher, J.M., 1983. "A direct approach to compensator design for distributed parameter systems," Other publications TiSEM 64c07d51-0d72-41c5-877e-7, Tilburg University, School of Economics and Management.
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