A Tree Structure Approach to Reachability Analysis

TL;DR

This paper introduces a tree-based reachability analysis method with geometric pruning to improve safety verification of autonomous systems, addressing the curse of dimensionality in moderate-dimensional problems.

Contribution

It presents a novel tree structure algorithm with geometric pruning that enhances reachability analysis efficiency for systems of moderate dimension.

Findings

The proposed method outperforms standard finite-difference approaches in numerical examples.

It effectively mitigates the curse of dimensionality for certain system classes.

Numerical comparisons demonstrate improved computational efficiency.

Abstract

Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of dimensionality. In this paper, we mitigate this problem for systems of moderate dimension and we propose a new algorithm based on a tree structure approach with geometric pruning. The numerical examples will include a comparison with a standard finite-difference method for linear and nonlinear problems