The value of timing information in event-triggered control

TL;DR

This paper investigates how timing information and communication delays affect the data rate needed for stabilizing linear plants via event-triggered control, revealing a phase transition in stabilization requirements.

Contribution

It introduces a phase transition analysis of the data rate for stabilization considering delay effects and provides explicit constructions for sufficient rates without probabilistic assumptions.

Findings

Timing information significantly reduces required data rate for small delays.

A critical delay threshold exists where timing information alone is insufficient.

When delay equals the inverse of the plant's entropy rate, the data-rate theorem applies.

Abstract

We study event-triggered control for stabilization of unstable linear plants over rate-limited communication channels subject to unknown, bounded delay. On one hand, the timing of event triggering carries implicit information about the state of the plant. On the other hand, the delay in the communication channel causes information loss, as it makes the state information available at the controller out of date. Combining these two effects, we show a phase transition behavior in the transmission rate required for stabilization using a given event-triggering strategy. For small values of the delay, the timing information carried by the triggering events is substantial, and the system can be stabilized with any positive rate. When the delay exceeds a critical threshold, the timing information alone is not enough to achieve stabilization and the required rate grows. When the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events, the delay equals the inverse of the entropy rate of the plant, and we obtain the same rate requirement prescribed by the data-rate theorem. When the delay is larger than this threshold, the required rate becomes larger than that required by the data-rate theorem. We also provide an explicit construction yielding a sufficient rate for stabilization, and generalize our results to vector systems. The results do not rely on any a priori probabilistic model of the delay or the initial conditions.