Event-Triggered Stabilization of Nonlinear Systems with Time-Varying Sensing and Actuation Delay

TL;DR

This paper introduces an event-triggered control strategy for nonlinear systems with time-varying delays, ensuring stabilization while reducing control updates and avoiding Zeno behavior, with proven stability and simulation validation.

Contribution

It develops a predictor-based event-triggered control method that guarantees stability for nonlinear systems with large, time-varying delays, extending existing delay compensation techniques.

Findings

Proves global asymptotic stability using Lyapunov methods.

Shows the event-triggered law has a uniform lower bound on inter-event times.

Demonstrates exponential stability for linear systems and analyzes convergence-rate trade-offs.

Abstract

This paper studies the problem of stabilization of a nonlinear system with time-varying delays in both sensing and actuation using event-triggered control. Our proposed strategy seeks to opportunistically minimize the number of control updates while guaranteeing stabilization and builds on predictor feedback to compensate for arbitrarily large known time-varying delays. We establish, using a Lyapunov approach, the global asymptotic stability of the closed-loop system as long as the open-loop system is globally input-to-state stabilizable in the absence of time delays and sampling. We further prove that the proposed event-triggered law has inter-event times that are uniformly lower bounded and hence does not exhibit Zeno behavior. For the particular case of a stabilizable linear system, we show global exponential stability of the closed-loop system and analyze the trade-off between the rate of exponential convergence and a bound on the sampling frequency. We illustrate these results in simulation and also examine the properties of the proposed event-triggered strategy beyond the class of systems for which stabilization can be guaranteed.