Reachability Analysis Using Hybrid Zonotopes and Functional Decomposition

TL;DR

This paper introduces a novel reachability analysis method for nonlinear systems using hybrid zonotopes and functional decomposition, achieving scalable computational complexity and improved efficiency over existing techniques.

Contribution

It combines hybrid zonotopes, state-update sets, and functional decomposition with new set identities to efficiently analyze nonlinear systems with linear growth in memory and linear scaling in computation.

Findings

Demonstrates effectiveness on benchmark examples

Achieves linear growth in memory complexity

Provides competitive performance compared to state-of-the-art

Abstract

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time and linear scaling in computational complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.