Boundary stabilization for a Heat-Kelvin-Voigt unstable interaction model, with control and partial observation localized on the interface only.

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. 2010 AMS: 74F10, 74K20, 76G25, 35B40, 35G25, 37L15