Reachability Analysis Using Hybrid Zonotopes and Functional Decomposition

• 成果类型: Article
• 署名作者: Siefert, Jacob A.; Bird, Trevor J.; Thompson, Andrew F.; Glunt, Jonah J.; Koeln, Justin P.; Jain, Neera; Pangborn, Herschel C.
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Texas System; University of Texas Dallas; Purdue University System; Purdue University; Purdue University in Indianapolis
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3528352
• 发表日期: 2025
• 页码: 4671-4686
• 关键词: Reachability analysis; vectors; Neural Networks; time complexity; Mechanical engineering; Hybrid power systems; scalability; Jacobian matrices; Generators; convex hulls; control systems; formal verification; nonlinear dynamical systems; reachability analysis; Set theory

摘要

This article proposes methods for reachability analysis of nonlinear systems, including those in closed loop with nonlinear controllers such as neural networks. 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 steps and linear scaling in time 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.