Title: Output Feedback Control of the One-Phase Stefan Problem

Speaker: Shumon Koga (UC San Diego) 

Abstract: When a solid-liquid material (e.g. ice and water) is melting
or freezing, the solid-liquid interface is moving due to its phase
transition. Such a problem is formulated by the one-phase Stefan
problem, which refers to a thermal diffusion partial differential
equation (PDE) defined on a time varying spatial domain whose dynamics
is actuated by the heat flux at the interface. In this presentation, a
backstepping observer and an output feedback control law designed for
the stabilization of the one-phase Stefan Problem will be addressed. We
propose a backstepping observer allowing to estimate the temperature
profile along the melting zone based on the available measurement,
namely, the solid phase length. The designed output feedback controller
ensures the exponential stability of the reference errors and
estimation errors of moving interface and the H1-norm of the
temperature profile with keeping physical constraints when the initial
estimation is chosen to satisfy some explicitly given conditions.