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

Irena Lasiecka (), Rasika Mahawattege () and Roberto Triggiani ()
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Irena Lasiecka: University of Memphis
Rasika Mahawattege: University of Maryland Baltimore County
Roberto Triggiani: University of Memphis

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 16, 1508 pages

Abstract: 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.

Keywords: Luenberger compensator; Stability; Control; Partial observation; Fluid–structure interaction; Interface; Boundary control; 74F10; 74K20; 76G25; 35B40; 35G25; 37L15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02477-4

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