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Event-based Boundary Control of One-phase Stefan Problem: A Static Triggering Approach

In liquid-solid phase change phenomena, the Stefan problem describes the time evolution of the material’s temperature profile and the interface position. This paper presents an event-based boundary control strategy for the one-phase Stefan problem. The proposed control approach consists of a full-state feedback backstepping boundary control law developed to drive the liquid-solid interface position to a desired setpoint and a static event-trigger mechanism which determines the time instants at which the control input needs to be updated. It is shown that the dwell-time between two triggering instances is uniformly bounded from below. Due to the existence of a minimal dwell-time, the closed-loop system is free from the so-called Zeno behavior. The control input is updated at event times and applied in a Zero-Order-Hold (ZOH) fashion. The well-posedness of the closed-loop system along with certain model validity conditions is proved. Furthermore, using the Lyapunov approach, it is shown that the proposed control approach globally exponentially stabilizes the temperature profile to the melting temperature of the material in L2-norm and the moving interface to the desired setpoint. A simulation example is provided to validate the theoretical developments.