Event-triggered Control of Infinite-dimensional Systems

TL;DR

This paper develops event-triggered control strategies for infinite-dimensional systems, ensuring stability and positive inter-event times, with methods tailored for systems with bounded and unbounded control operators.

Contribution

It introduces novel event-triggering mechanisms for infinite-dimensional systems, guaranteeing stability and positive inter-event times under various operator conditions.

Findings

Positive lower bound on inter-event times for compact feedback operators

Exponential stability achieved with small thresholds in event-triggering mechanisms

Two new event-triggering methods for unbounded control operators

Abstract

This paper addresses the problem of event-triggered control for infinite-dimensional systems. We employ event-triggering mechanisms that compare the plant state and the error of the control input induced by the event-triggered implementation. Under the assumption that feedback operators are compact, a strictly positive lower bound on the inter-event times can be guaranteed. We show that if the threshold of the event-triggering mechanisms is sufficiently small, then the event-triggered control system with a bounded control operator and a compact feedback operator is exponentially stable. For infinite-dimensional systems with unbounded control operators, we employ two event-triggering mechanisms that are based on system decomposition and periodic event-triggering, respectively, and then analyze the exponential stability of the closed-loop system under each event-triggering mechanism.