The Curious Case of Integrator Reach Sets, Part I: Basic Theory

• 成果类型: Article
• 署名作者: Haddad, Shadi; Halder, Abhishek
• 署名单位: University of California System; University of California Santa Cruz
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3244694
• 发表日期: 2023
• 页码: 6680-6695
• 关键词: Convex geometry; integrator; reach set; set-valued uncertainty.

摘要

This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof. In this Part I, assuming box-valued input uncertainties, we establish that this compact convex reach set is semialgebraic, translated zonoid, and not a spectrahedron. We derive the parametric as well as the implicit representation of the boundary of this reach set. We also deduce the closed-form formula for the volume and diameter of this set, and discuss their scaling with state dimension and time. We point out that these results may be utilized in benchmarking the performance of the reach set overapproximation algorithms.