Minimally Constrained Stable Switched Systems and Application to Co-simulation

TL;DR

This paper introduces an algorithm to restrict switching signals in constrained switched systems to ensure stability while maximizing allowed behaviors, with applications to co-simulation stability certification.

Contribution

It presents a novel method for constraining switching signals to guarantee stability without overly restricting system behavior, specifically applied to co-simulation stability.

Findings

Algorithm successfully guarantees stability in constrained switched systems.

Application to adaptive co-simulation demonstrates effective stability certification.

Maximizes the set of allowed switching signals while maintaining stability.

Abstract

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.