Abstracting the Traffic of Nonlinear Event-Triggered Control Systems

TL;DR

This paper develops a method to abstract and schedule traffic in nonlinear event-triggered control systems with uncertainties, enabling better network communication management through reachability analysis and isochronous manifold-based partitioning.

Contribution

It extends existing frameworks by introducing abstractions for uncertain nonlinear ETC systems using novel partitioning and reachability algorithms.

Findings

Effective abstraction of nonlinear uncertain ETC systems.

Tighter intersampling time intervals via isochronous manifolds.

Simulations demonstrate improved scheduling accuracy.

Abstract

Scheduling communication traffic in networks of event-triggered control (ETC) systems is challenging, as their sampling times are unknown, hindering application of ETC in networks. In previous work, finite-state abstractions were created, capturing the sampling behaviour of LTI ETC systems with quadratic triggering functions. Offering an infinite-horizon look to all sampling patterns of an ETC system, such abstractions can be used for scheduling of ETC traffic. Here we significantly extend this framework, by abstracting perturbed uncertain nonlinear ETC systems with general triggering functions. To construct an ETC system's abstraction: a) the state space is partitioned into regions, b) for each region an interval is determined, containing all intersampling times of points in the region, and c) the abstraction's transitions are determined through reachability analysis. To determine intervals and transitions, we devise algorithms based on reachability analysis. For partitioning, we propose an approach based on isochronous manifolds, resulting into tighter intervals and providing control over them, thus containing the abstraction's non-determinism. Simulations showcase our developments.