Completeness of Riemannian metrics: an application to the control of constrained mechanical systems

[2311.14969] Completeness of Riemannian metrics: an application to the control of constrained mechanical systems Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2311.14969 (eess) [Submitted on 25 Nov 2023] Title: Completeness of Riemannian metrics: an application to the control of constrained mechanical systems Authors: José Ángel Acosta , Anthony Bloch , David Martín de Diego View PDF HTML (experimental) Abstract: We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems. In essence our result is based on the construction of a complete Riemannian metric in the modified space where the constraint is included. In particular this can be applied to the controlled Lagrangians technique Bloch et al. [2000b, 2001] modifying its metric to additionally cover mechanical systems with configuration constraints via control. The technique used consists of approximating incomplete Riemannian metrics by complete ones, modifying the evolution near a boundary and finding a controller satisfying a given design criterion. Comments: 18 pages, 11 figures Subjects: Systems and Control (eess.SY) ; Differential Geometry (math.DG); Dynamical Systems (math.DS) MSC classes: 53C, 53Z Cite as: arXiv:2311.14969 [eess.SY] (or arXiv:2311.14969v1 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2311.14969 Focus to learn more arXiv-issued DOI via DataCite Journal reference: IEEE Transactions on Automatic Control (2026) Related DOI : https://doi.org/10.1109/TAC.2025.3595000 Focus to learn more DOI(s) linking to related resources Submission history From: José Ángel Acosta [ view email ] [v1] Sat, 25 Nov 2023 09:04:13 UTC (1,443 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2023-11 Change to browse by: cs cs.SY eess math math.DG math.DS References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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