Compositional Construction of Barrier Functions for Switched Impulsive Systems
Abstract
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid collisions with obstacles), barrier functions are widely utilized. As the system dimension increases, deriving suitable barrier functions becomes extremely complex. Fortunately, many systems consist of multiple subsystems, such as different areas where the disease occurs. In this work, we present sufficient conditions for interconnected switched impulsive systems to maintain safety by constructing local barrier functions for the individual subsystems instead of a global one, allowing for much easier and more efficient derivation. To validate our results, we numerically demonstrate its effectiveness using an epidemiological model.
Cite
@article{arxiv.2407.20084,
title = {Compositional Construction of Barrier Functions for Switched Impulsive Systems},
author = {Katharina Bieker and Hugo Tadashi Kussaba and Philipp Scholl and Jaesug Jung and Abdalla Swikir and Sami Haddadin and Gitta Kutyniok},
journal= {arXiv preprint arXiv:2407.20084},
year = {2024}
}
Comments
Accepted for publication in the proceedings of the IEEE 63rd Conference on Decision and Control