Event-triggered Observability: A Set-membership Perspective

TL;DR

This paper introduces a new concept of $$-observability for linear systems with event-triggered measurements, developing criteria and an observer that efficiently estimates states using set-membership methods under event-triggered conditions.

Contribution

It proposes the novel $$-observability notion, develops a criterion for it, and designs an optimal set-membership observer that accounts for event-triggered communication.

Findings

The $$-observability criterion effectively tests system observability under event-triggered conditions.

The set-membership observer provides asymptotically bounded state estimates.

Numerical experiments demonstrate the observer's efficiency and accuracy.

Abstract

This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $\epsilon$-observability is defined with parameter $\epsilon$, which relates to the worst-case performance of inferring the initial state based on not only the received measurement but also the implicit information in the event-triggering conditions at no-event instants. A criterion is developed to test the proposed $\epsilon$-observability of discrete-time linear systems, based on which an iterative event-triggered set-membership observer is designed to evaluate a set containing all possible values of the state. The proposed set-membership observer is designed as the outer approximation of the ellipsoids predicted based on previous state estimates and the ellipsoids inferred by fusing the received measurement and communication conditions, which is optimal in the sense of trace at each step and is proved to be asymptotically bounded. The efficiency of the proposed event-triggered set-membership state observer is verified by numerical experiments.