Convex Hulls of Reachable Sets

[2303.17674] Convex Hulls of Reachable Sets Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2303.17674 (math) [Submitted on 30 Mar 2023 ( v1 ), last revised 14 Apr 2026 (this version, v5)] Title: Convex Hulls of Reachable Sets Authors: Thomas Lew , Riccardo Bonalli , Marco Pavone View a PDF of the paper titled Convex Hulls of Reachable Sets, by Thomas Lew and 2 other authors View PDF HTML (experimental) Abstract: We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation with initial conditions on the sphere. This finite-dimensional characterization unlocks an efficient sampling-based estimation algorithm to accurately over-approximate reachable sets. We also study the structure of the boundary of the reachable convex hulls and derive error bounds for the estimation algorithm. We give applications to neural feedback loop analysis and robust MPC. Comments: 20 pages. IEEE Transactions on Automatic Control 2025. Simplified maximality condition (no minus sign) Subjects: Optimization and Control (math.OC) ; Machine Learning (cs.LG); Robotics (cs.RO); Systems and Control (eess.SY) Cite as: arXiv:2303.17674 [math.OC] (or arXiv:2303.17674v5 [math.OC] for this version) https://doi.org/10.48550/arXiv.2303.17674 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Thomas Lew [ view email ] [v1] Thu, 30 Mar 2023 19:31:41 UTC (2,393 KB) [v2] Fri, 21 Jul 2023 19:28:01 UTC (2,822 KB) [v3] Thu, 29 Feb 2024 16:14:01 UTC (7,918 KB) [v4] Sat, 27 Jul 2024 21:13:14 UTC (3,861 KB) [v5] Tue, 14 Apr 2026 21:26:19 UTC (3,615 KB) Full-text links: Access Paper: View a PDF of the paper titled Convex Hulls of Reachable Sets, by Thomas Lew and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2023-03 Change to browse by: cs cs.LG cs.RO cs.SY eess eess.SY math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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