Compositional Construction of Barrier Functions for Switched Impulsive Systems

TL;DR

This paper introduces a method for constructing local barrier functions for interconnected switched impulsive systems, simplifying safety verification in complex, high-dimensional systems like epidemiological models.

Contribution

It provides sufficient conditions for safety via local barrier functions, reducing complexity compared to global approaches.

Findings

Effective local barrier functions derived for interconnected systems

Numerical validation using an epidemiological model

Simplifies safety verification in high-dimensional 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.