Sampled-data reachability analysis using sensitivity and mixed-monotonicity
Abstract
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discrete-time approach relying on a mixed-monotonicity property. We then present a new over-approximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulation-based approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.
Cite
@article{arxiv.1803.02214,
title = {Sampled-data reachability analysis using sensitivity and mixed-monotonicity},
author = {Pierre-Jean Meyer and Samuel Coogan and Murat Arcak},
journal= {arXiv preprint arXiv:1803.02214},
year = {2021}
}