Robustifying Event-Triggered Control to Measurement Noise

TL;DR

This paper introduces a comprehensive framework for designing measurement noise-robust event-triggered control systems that prevent Zeno behavior and ensure practical stability, applicable to various control problems.

Contribution

It presents a general approach for robust event-triggered control under measurement noise, including static and dynamic rules, with proofs of Zeno-freeness and applicability to existing schemes.

Findings

Framework guarantees Zeno-free operation with positive inter-event time bounds.

Existing control schemes can be redesigned for noise robustness using the proposed framework.

Simulation results demonstrate effectiveness of the noise-robust event-triggered control methods.

Abstract

While many event-triggered control strategies are available in the literature, most of them are designed ignoring the presence of measurement noise. As measurement noise is omnipresent in practice and can have detrimental effects, for instance, by inducing Zeno behavior in the closed-loop system and with that the lack of a positive lower bound on the inter-event times, rendering the event-triggered control design practically useless, it is of great importance to address this gap in the literature. To do so, we present a general framework for set stabilization of (distributed) event-triggered control systems affected by additive measurement noise. It is shown that, under general conditions, Zeno-free static as well as dynamic triggering rules can be designed such that the closed-loop system satisfies an input-to-state practical set stability property. We ensure Zeno-freeness by proving the existence of a uniform strictly positive lower-bound on the minimum inter-event time. The general framework is applied to point stabilization and consensus problems as particular cases, where we show that, under similar assumptions as the original work, existing schemes can be redesigned to robustify them to measurement noise. Consequently, using this framework, noise-robust triggering conditions can be designed both from the ground up and by simple redesign of several important existing schemes. Simulation results are provided that illustrate the strengths of this novel approach.