[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82796-en":3,"doc-seo-82796-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},82796,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Robust Receding Horizon Games with Additive Uncertainty","Study a receding horizon game with multiple agents controlling linear systems under additive disturbances, private state/input limits, and shared coupling constraints. Present a robust game-theoretic control framework combining tube-based constraint tightening with a finite-horizon generalized Nash equilibrium problem using a DARE-based terminal cost and a decoupled positively invariant terminal set. Provide guarantees of recursive feasibility for any bounded disturbance realization. Using a potential-game structure from tracking costs, show nominal states converge to a steady-state variational GNE while actual states converge to a neighborhood defined by the minimal robust positively invariant set.","Robust Receding Horizon Games with Additive  \nUncertainty  \nDinesh Patra, Tanish Jain and Ashish R. Hota  \narXiv :2607 .04213v1 [math .OC] 5 Jul 2026  \nAbstract—We study a receding horizon game in which multiple agents drive linear systems subject to additive disturbances, private state and input constraints, and shared coupling constraints. We propose a robust game-theoretic control framework that combines tube-based constraint tightening with a finite-horizon generalized Nash equilibrium problem (GNEP), equipped with a discrete algebraic Riccati equation (DARE)-based terminal cost and a decoupled positively invariant terminal set. The framework guarantees recursive feasibility for every bounded disturbance realization. Exploiting the potential-game structure induced by tracking costs, we further establish asymptotic convergence of each agent’s nominal state to a steady-state variational generalized Nash equilibrium (vGNE), and show that each agent’s actual state converges to a neighborhood of the vGNE determined by the minimal robust positively invariant set.  \nIndex Terms—Receding horizon games, robust model predictive control, generalized Nash equilibrium, potential games.  \nI. INTRODUCTION  \nModern engineered systems such as smart power grids, autonomous vehicles, and industrial robots increasingly rely on the interplay of competition and coordination among many agents operating in a shared uncertain environment. As the number of agents grows, relying on a single centralized controller becomes intractable. Instead, each agent needs to optimize its own objective while satisfying both private constraints and constraints it shares with others. For an individual agent, deploying a receding horizon or model predictive control (MPC) scheme is a natural choice because it explicitly handles constraints and provides rigorous guarantees on closed-loop behavior. Therefore, the study of game-theoretic interaction among agents that individually run receding horizon controllers is a problem of considerable practical relevance.  \nConsequently, the receding horizon games (RHG) framework has attracted growing interest in recent years. References [1]–[3] explored game-theoretic planning for autonomous racing and self-driving cars, while Mignoni et al. [4] applied related ideas to energy management. The first rigorous treatments of recursive feasibility and stability in RHGs appeared in [5],[6] . The initial work [5] established recursive feasibility and stability through a connection to potential games but relied on terminal equality constraints. The follow-up work [6] proved stability under input coupling and input constraints for general economic costs, and did not consider constraints on the states or disturbance affecting the dynamics. Benenati and  \nD. Patra and A. R. Hota are with the Department of Electrical Engineering, Indian Institute of Technology (IIT) Kharagpur, India. T. Jain was with the Department of Aerospace Engineering, IIT Kharagpur, India. Email: [dinesh.patra912@kgpian.iitkgp.ac.in](dinesh.patra912@kgpian.iitkgp.ac.in), [jtanish120204@gmail.com](jtanish120204@gmail.com), [ahota@ee.iitkgp.ac.in](ahota@ee.iitkgp.ac.in).  \nGrammatico [7] subsequently studied linear-quadratic dynamic games as receding-horizon variational inequalities.  \nThe above works consider deterministic linear dynamical systems that are not affected by any disturbance or uncertainty. In the single-agent setting, robust MPC under additive disturbances have been studied extensively [8]–[10] . Among various robust MPC techniques, tube-based approaches [11]–[13] provide an elegant solution by confining the uncertain states to a tube around a nominal trajectory, and establish recursive feasibility and stability guarantees by tightening the constraints.  \nRobust MPC for multiple agents has been studied largely in the cooperative distributed setting, where agents jointly minimize a system-wide objective rather than their own costs. The tube-based treatment ","cbCainme5q1Gnnkw","https://ap.wps.com/l/cbCainme5q1Gnnkw","pdf",255985,1,"English","en",105,"# Introduction\n## Motivation and motivation gap\n## Related work in receding-horizon and robust MPC\n## Contributions and problem setup","[{\"question\":\"What problem does the paper address in multi-agent control?\",\"answer\":\"The paper studies receding horizon games where multiple agents control linear systems with additive disturbances and private constraints while also satisfying shared coupling constraints.\"},{\"question\":\"What robust control framework is proposed?\",\"answer\":\"It combines tube-based constraint tightening with a finite-horizon generalized Nash equilibrium problem, using a DARE-based terminal cost and a decoupled positively invariant terminal set.\"},{\"question\":\"What convergence and feasibility guarantees are established?\",\"answer\":\"The framework guarantees recursive feasibility for any bounded disturbance realization, and under the potential-game structure it proves nominal-state convergence to a steady variational GNE and actual-state convergence to a neighborhood characterized by a minimal robust positively invariant 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problem does the paper address in multi-agent control?","Question",{"text":74,"@type":75},"The paper studies receding horizon games where multiple agents control linear systems with additive disturbances and private constraints while also satisfying shared coupling constraints.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What robust control framework is proposed?",{"text":79,"@type":75},"It combines tube-based constraint tightening with a finite-horizon generalized Nash equilibrium problem, using a DARE-based terminal cost and a decoupled positively invariant terminal set.",{"name":81,"@type":72,"acceptedAnswer":82},"What convergence and feasibility guarantees are established?",{"text":83,"@type":75},"The framework guarantees recursive feasibility for any bounded disturbance realization, and under the potential-game structure it proves nominal-state convergence to a steady variational GNE and actual-state convergence to a neighborhood characterized by a minimal robust 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