{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/data-driven-control-of-t-product-based","title":"Data-driven Control of T-Product-based Dynamical Systems","arxiv_id":"2502.14591","date":"2025-02-20","proceeding":null,"authors":["Ziqin He","Yidan Mei","Shenghan Mei","Xin Mao","Anqi Dong","Ren Wang","Can Chen"],"abstract":"Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as stabilization, linear quadratic regulation, and model predictive control, have been extensively developed, these methods are not inherently suited for multi-linear dynamical systems, where the states are represented as higher-order tensors. In this article, we propose a novel framework for data-driven control of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we offer necessary and sufficient conditions to determine the data informativity for system identification, stabilization by state feedback, and T-product quadratic regulation of TPDSs with detailed complexity analyses. Finally, we validate our framework through numerical examples.","url_abs":"https://arxiv.org/abs/2502.14591v1","url_pdf":"https://arxiv.org/pdf/2502.14591v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"data-driven-control-of-t-product-based","repo_url":"https://github.com/ZiqinHe/TPDSn","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-predictive-control","task_name":"Model Predictive Control"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}