Speaker:  Xiang Wan (Loyola University Chicago)

 Title: Luenberger Dynamic Compensator: Theory and Applications to Heat-Structure Interaction

 Abstract:

In this talk, we will discuss recent developments in the continuous theory of the Luenberger dynamic compensator, also known as a state estimator or state observer. The focus will be on its application to a class of Heat-Structure Interaction (HIS) Partial Differential Equation (PDE) models with high Kelvin-Voigt damping. Physically the model occupies a doughnut-like domain: the heat (fluid) occupies the exterior domain while the structure (wave) occupies an interior subdomain.

We will explore scenarios where feedback control is applied either at the interface between the two media or at the external boundary of the physical domain. We will analyze three different cases of controls: (i) Neumann at the interface, (ii) Dirichlet at the interface, and (iii) Dirichlet at the external boundary. We will also discuss some very recent results where partial observation is located only on a small part of the interface between two environments, and the control action is localized on another part of the interface.