Event-Triggered Safe Stabilizing Boundary Control for the Stefan PDE System with Actuator Dynamics

TL;DR

This paper develops an event-triggered boundary control method for the Stefan PDE system with actuator dynamics, ensuring safety and stability while avoiding Zeno behavior through a dwell-time mechanism.

Contribution

It introduces an event-triggered control scheme with safety guarantees for the Stefan PDE system, combining ZOH, Control Barrier Functions, and PDE backstepping.

Findings

Zeno behavior is avoided with a minimum dwell-time proof.

Control ensures safe stabilization of the Stefan PDE system.

Numerical simulations confirm effectiveness.

Abstract

This paper proposes an event-triggered boundary control for the safe stabilization of the Stefan PDE system with actuator dynamics. The control law is designed by applying Zero-Order Hold (ZOH) to the continuous-time safe stabilizing controller developed in our previous work. The event-triggering mechanism is then derived so that the imposed safety conditions associated with high order Control Barrier Function (CBF) are maintained and the stability of the closed-loop system is ensured. We prove that under the proposed event-triggering mechanism, the so-called ``Zeno" behavior is always avoided, by showing the existence of the minimum dwell-time between two triggering times. The stability of the closed-loop system is proven by employing PDE backstepping method and Lyapunov analysis. The efficacy of the proposed method is demonstrated in numerical simulation.