Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control

[2606.23250] Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2606.23250 (math) [Submitted on 22 Jun 2026 ( v1 ), last revised 22 Aug 2026 (this version, v3)] Title: Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control Authors: Anders Hansson , Johan Löfberg View PDF HTML (experimental) Abstract: We study a sparse linear-quadratic problem for transportation dynamics. The sparsity pattern has a natural directed-graph representation in which vertices are storage locations and edges are transportation links. The goal is to compute the optimal control signal without applying the usually dense optimal feedback gain directly. We show that the optimal feedback gain can be factorized as the product of a sparse matrix and the inverse of another sparse matrix from the right. In contrast to an existing factorization that uses an inverse from the left, the proposed factors use graph-adapted state coordinates. When the underlying graph is a tree, we give, for every edge orientation, a closed formula for the Riccati matrix that determines these factors and a graph-based bound on their possible nonzero entries. This factorization can reduce the online cost relative to dense feedback multiplication and permits distributed evaluation. The main message is that linear quadratic control need not appear dense when expressed in graph-adapted coordinates, and that these coordinates can reveal intrinsic sparsity. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2606.23250 [math.OC] (or arXiv:2606.23250v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2606.23250 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anders Hansson [ view email ] [v1] Mon, 22 Jun 2026 12:32:28 UTC (26 KB) [v2] Fri, 26 Jun 2026 15:01:02 UTC (28 KB) [v3] Sat, 22 Aug 2026 08:28:38 UTC (40 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-06 Change to browse by: math 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)

Related documents

• Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control#665824
• Traffic Congestion Control for ARZ Model with an Arbitrarily Large Input Delay#926273
• Residual Learning-Based Control of Vehicle Platoons with $\ell_2$ Stability Guarantees via Recurrent Equilibrium Networks#1118965
• Stochastic Robust Linear W-infinity Control via Dynamic Output Feedback#662481
• Stochastic Robust Linear W-infinity Control via Dynamic Output Feedback#661431