Sampled-Data Output Feedback Control of the Stefan Problem with Explicit Condition of Sampling Scheduling

This paper provides sampled-data output feed-back control of the Stefan problem with an explicit condition of sampling scheduling. The Stefan problem is a well-known physical model of the liquid-solid phase change, governed by a parabolic partial differential equation (PDE) of the temperature profile over a moving domain governed by an Ordinary Differential Equation (ODE). Utilizing two measurements of the liquid-solid interface position and the temperature gradient at the interface position for all time, we design a continuous-time PDE backstepping observer to estimate true temperature profile. Then, the output feedback control law is given based on the temperature estimate, and the sampled-data input is executed as Zero-Order-Hold (ZOH). Under the explicit condition of sampling scheduling, we rigorously prove that the closed-loop system is well-posed and satisfies the required condition of the physical model, and is exponentially stable. Numerical results are provided to illustrate the effectiveness of the proposed method.