Boundary Control and Estimation of the One-Phase Stefan Problem

In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan Problem, which stands stand as an improvement of the recent full state feedback backstepping controller proposed in our previous contribution. The onephase Stefan Problem describes time evolution of a temperature profile in a solid-liquid material and its solid-liquid moving interface, which is formulated by a 1-D diffusion Partial Differential Equation (PDE) defined on a time-varying spatial domain described by an ordinary differential equation (ODE). The proposed backstepping observer allows to estimate the temperature profile along the melting zone based on the available measurement, namely, the solid phase length. The output feedback controller ensures the exponential stability of the moving interface, the H-norm of the distributed temperature, and the estimation errors with keeping physical constraints when the initial value are compatible to some explicitly given restrictions.