Divide and Conquer: Variable Set Separation in Hybrid Systems Reachability Analysis

TL;DR

This paper introduces a method to improve the scalability of hybrid systems reachability analysis by dividing the state space into sub-spaces and performing computations locally, enhancing efficiency and precision.

Contribution

It formalizes a novel divide-and-conquer algorithm for reachability analysis and evaluates its performance against traditional global space methods.

Findings

Improved computational efficiency in high-dimensional systems

Enhanced precision in reachability results

Demonstrated scalability benefits through experimental evaluation

Abstract

In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets in an over-approximative manner. As the computational costs steeply increase with the dimension, in this work we analyse the possibilities for improving scalability by dividing the search space in sub-spaces and execute reachability computations in the sub-spaces instead of the global space. We formalise such an algorithm and provide experimental evaluations to compare the efficiency as well as the precision of our sub-space search to the original search in the global space.