Event-triggered second-moment stabilization of linear systems under packet drops

TL;DR

This paper proposes an event-triggered transmission policy for stabilizing linear systems with process noise under packet drops, ensuring exponential convergence of the second moment of the state with resource-efficient communication.

Contribution

It introduces a novel event-triggering approach tailored to control objectives, guaranteeing stability and quantifying transmission efficiency under packet drop conditions.

Findings

Ensures exponential second-moment stability with finite-time convergence.

Provides an upper bound on expected transmission fraction.

Validates results through simulations on scalar and vector systems.

Abstract

This paper deals with the stabilization of linear systems with process noise under packet drops between the sensor and the controller. Our aim is to ensure exponential convergence of the second moment of the plant state to a given bound in finite time. Motivated by considerations about the efficient use of the available resources, we adopt an event-triggering approach to design the transmission policy. In our design, the sensor's decision to transmit or not the state to the controller is based on an online evaluation of the future satisfaction of the control objective. The resulting event-triggering policy is hence specifically tailored to the control objective. We formally establish that the proposed event-triggering policy meets the desired objective and quantify its efficiency by providing an upper bound on the fraction of expected number of transmissions in an infinite time interval. Simulations for scalar and vector systems illustrate the results.