Lower Bound of Networked Control with Multiple Sensors and One Controller And The Application to Tracking Gaussian-Markov Source

[2607.04172] Lower Bound of Networked Control with Multiple Sensors and One Controller And The Application to Tracking Gaussian-Markov Source Skip to main content Search Submit Donate Log in Computer Science > Information Theory arXiv:2607.04172 (cs) [Submitted on 5 Jul 2026] Title: Lower Bound of Networked Control with Multiple Sensors and One Controller And The Application to Tracking Gaussian-Markov Source Authors: Sijie Li , Takashi Tanaka , Hyeji Kim View PDF HTML (experimental) Abstract: This paper investigates the causal rate-distortion function for networked control systems with multiple encoders and a single decoder, a longstanding open problem in information and control theory. While previous work has explored the causal rate-distortion function for single-encoder and feedback-enabled networked settings, the case of networks without feedback remains unaddressed. We establish a novel directed information lower bound, the first derived for the networked control setting. We further demonstrate the optimality of linear, independent encoders and linear decoders for optimizing this lower bound for Linear Quadratic Gaussian (LQG) plant and quadratic cost, with the condition that the full plant state is observed when sensors are sitting together. By reducing the original infinite-dimensional optimization problem to a finite-dimensional one, our approach simplifies the analysis. Additionally, our directed information lower bound provides an alternate proof for the sufficiency of linear encoders in the single encoder and single decoder setting with side information, extending prior results in the literature. We present Semidefinite Programming formulations for the causal rate distortion function of Gaussian-Markov sources with linear side information and the singular noise matrix. Comments: 36 pages, 3 figures, partially presented at ISIT 2025, submitted to TAC Subjects: Information Theory (cs.IT) ; Systems and Control (eess.SY) Cite as: arXiv:2607.04172 [cs.IT] (or arXiv:2607.04172v1 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2607.04172 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sijie Li [ view email ] [v1] Sun, 5 Jul 2026 08:40:45 UTC (144 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.IT < prev | next > new | recent | 2026-07 Change to browse by: cs cs.SY eess eess.SY math math.IT 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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