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Performace-barrier-based event-triggered boundary control of a class of reaction-diffusion PDEs
B. Rathnayake, M. Diagne, J. Cortés, M. Krstic
Proceedings of the American Control Conference, Toronto, Canada, 2024, submitted

Abstract

This paper presents a novel event-triggered boundary control technique named performance-barrier-based event-triggered boundary control for a class of reaction-diffusion PDEs with Robin actuation. At its core, rather than insisting on a strictly monotonic decrease of the Lyapunov function for the closed-loop system, we allow it to increase as long as it remains within an established performance barrier. This approach integrates a performance residual-the difference between the performance barrier and the Lyapunov function-into the triggering mechanism. This integration provides the system's Lyapunov function with enhanced flexibility, thereby allowing for longer dwell-times compared to strategies demanding a monotonic decrease of the Lyapunov function. Notably, while adhering to the performance barrier, the closed-loop system converges to zero globally in L2-sense without encountering the Zeno phenomenon. We provide numerical simulations to demonstrate the effectiveness of our technique against the regular event-triggered boundary control design, the latter being associated with strictly decreasing Lyapunov functions.

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