Nonlinear Dynamic Periodic Event-Triggered Control with Robustness to Packet Loss Based on Non-Monotonic Lyapunov Functions

TL;DR

This paper introduces a nonlinear periodic event-triggered control method that ensures robust stabilization of systems despite packet loss, utilizing non-monotonic Lyapunov functions for improved sampling and trigger design.

Contribution

It presents a novel PETC mechanism based on non-monotonic Lyapunov functions that guarantees stability and robustness to packet loss, with a new approach for sampling period determination.

Findings

Guarantees worst-case convergence behavior with tunable deviations

Integrates packet loss considerations into PETC design

Demonstrates effectiveness through a nonlinear numerical example

Abstract

This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic event-triggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a dynamic, state dependent PETC mechanism is designed. The proposed mechanism guarantees on average the same worst case convergence behavior except for tunable deviations. Furthermore, a new approach to determine the sampling period for the proposed PETC mechanism is presented. This approach as well as the actual trigger rule exploit the theory of non-monotonic Lyapunov functions. An additional feature of the proposed PETC mechanism is the possibility to integrate knowledge about packet losses in the PETC design. The proposed PETC mechanism is illustrated with a nonlinear numerical example from literature. This paper is the accepted version of [1], containing also the proofs of the main results.