Abstracting the Traffic of Nonlinear Event-Triggered Control Systems

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 behavior of linear time-invariant (LTI) ETC systems with quadratic triggering functions. Offering an infinite-horizon look to ETC systems' sampling patterns, 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: 1) the state space is partitioned into regions; 2) for each region, an interval is determined, containing all intersampling times of points in the region; and 3) 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 nondeterminism. Simulations showcase our developments.

Automated summary

This article investigates the scheduling of communication traffic in networks of event-triggered control systems. By abstracting perturbed uncertain nonlinear ETC systems with general triggering functions, the authors propose algorithms based on reachability analysis to determine intervals and transitions for the system's abstraction. They also propose an approach based on isochronous manifolds for partitioning, which results in tighter intervals and provides control over them, reducing the abstraction's nondeterminism. Simulation results demonstrate the effectiveness of the proposed method.