Trade-Offs in Stochastic Event-Triggered Control

TL;DR

This paper investigates the balance between communication reduction and control performance in stochastic event-triggered control systems for linear plants, providing analytical trade-off expressions and numerical validation.

Contribution

It introduces a control policy design that minimizes quadratic costs while maintaining Gaussian properties under stochastic event-triggering, with explicit trade-off analysis.

Findings

Analytical expressions for communication-control trade-off.

Quantitative validation through numerical examples.

Preservation of Gaussian properties in control systems.

Abstract

This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the trade-off between the communication cost and control performance of such event-triggered control systems. This trade-off is confirmed quantitatively via numerical examples.