[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85404-en":3,"doc-seo-85404-105":29,"detail-sidebar-cat-0-en-105":91},{"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":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85404,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782109480056885918",8,"Research & Report","Stochastic MPC with Online-optimized Policies and Closed-loop Guarantees","Stochastic model predictive control for linear systems with additive Gaussian disturbances is developed using online optimization of disturbance feedback matrices. The method enforces probabilistic (chance) constraints while guaranteeing recursive feasibility of the underlying convex optimization in closed loop. By optimizing feedback policies online, the approach improves performance and reduces conservatism versus fixed-feedback alternatives. A finitely determined maximal admissible set and time-varying reconditioning of predicted probabilistic constraints on current knowledge drive the guarantees. Applicability is shown through building temperature control.","Stochastic MPC with Online-optimized Policies and  \nClosed-loop Guarantees  \nMarcell Bartos, Alexandre Didier, Jerome Sieber, Johannes Khler†, Melanie N. Zeilinger†  \narXiv :2502 .06469v3 [ ee ss . SY] 12 Jul 2026  \nAbstract—This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances that optimizes over disturbance feedback matrices online. Closed-loop satisfaction of probabilistic constraints and recursive feasibility of the underlying convex optimization problem is guaranteed. Optimization over feedback policies online increases performance and reduces conservatism compared to fixed-feedback approaches. The central mechanism is a finitely determined maximal admissible set for probabilistic constraints, together with the reconditioning of the predicted probabilistic constraints on the current knowledge at every time step. The proposed method’s applicability is demonstrated on a building temperature control example.  \nIndex Terms—Predictive control for linear systems, chance constraints, stochastic optimal control, constrained control  \nI. INTRODUCTION  \nModel predictive control (MPC) [1], [2] is a powerful approach for the optimal control of constrained systems, by solving finite horizon optimization problems in a receding horizon manner. For deterministic systems, MPC offers strong theoretical guarantees in terms of constraint satisfaction, stability, and performance. However, ensuring constraint satisfaction for stochastic dynamical systems is challenging. To address this issue, stochastic MPC (SMPC) schemes [3],[4] consider a probabilistic description of the uncertainty and enforce safetycritical constraints with a user-chosen probability. In this work, we propose an SMPC scheme for linear time-invariant systems affected by additive Gaussian disturbances that  \na) improves performance by using online-optimized affine feedback policies while preserving convexity,  \nb) and guarantees recursive feasibility and satisfaction of the chance constraints in closed loop.  \nRelated work: If the support of the distribution of the disturbance is bounded, recursive feasibility of SMPC optimization problems can be ensured by adopting robust constraint tightening approaches, see, e.g., [5], [6] . However, in the unbounded support case (such as the Gaussian distribution considered in this paper), guaranteeing recursive feasibility becomes nontrivial [3], [7] . A common solution is to use recovery mechanisms [8], or soften the constraints [9], but this often leads to the loss of closed-loop chance constraint satisfaction  \n† : joint supervision. All authors are with the Institute for Dynamic Systems and Control, ETH Zurich, 8092 Z¨urich, Switzerland (e-mail: [mbartos, adidier, jsieber, mzeilinger]@[ethz.ch](ethz.ch), [j.kohler@imperial.ac.uk](j.kohler@imperial.ac.uk)). Johannes Khler has been supported by the Swiss National Science Foundation under NCCR Automation (grant agreement 51NF40 180545) . This work was supported as a part of NCCR Automation, a National Centre of Competence in Research, funded by the Swiss National Science Foundation (grant number 51NF40 225155) .  \nguarantees, unless stronger assumptions are used [10]–[12] . In contrast, the methods of [13]–[15] achieve property b) via the so-called indirect feedback paradigm. These methods do not initialize the predicted trajectories that enter the constraints of the optimization problem based on the current measurement of the state, i.e., they do not recondition on current knowledge. Instead, they use the shifted optimal nominal state from the previous solution for initialization, and use a separate predicted trajectory for the cost function, which is initialized by the true state. All of the aforementioned methods that achieve b) rely on offline-designed feedback policies to construct probabilistic reachable sets, and thus they do not offer a), which limits their performance.  \nAs for requirement a), the advantag","cbCaitI8HaKPMCca","https://ap.wps.com/l/cbCaitI8HaKPMCca","pdf",2858050,1,16,"English","en",105,"# Introduction\n## Problem Setting and Motivation\n## Related Work and Gaps","[{\"question\":\"What type of systems and uncertainty does the proposed stochastic MPC address?\",\"answer\":\"It targets linear time-invariant systems subject to additive Gaussian disturbances and uses a probabilistic description of uncertainty to handle constraints.\"},{\"question\":\"How does the method guarantee closed-loop satisfaction of probabilistic constraints?\",\"answer\":\"It uses a finitely determined maximal admissible set for probabilistic constraints and reconditions the predicted probabilistic constraints at every time step based on current knowledge.\"},{\"question\":\"What is the key benefit of optimizing feedback policies online compared with fixed-feedback approaches?\",\"answer\":\"Online optimization over disturbance feedback policies improves performance and reduces conservatism while maintaining recursive feasibility for the chance-constrained convex optimization problem.\"}]",1784203165,40,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"stochastic-mpc-with-online-optimized-policies-and-closed-loop-guarantees","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/stochastic-mpc-with-online-optimized-policies-and-closed-loop-guarantees/85404/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What type of systems and uncertainty does the proposed stochastic MPC address?","Question",{"text":75,"@type":76},"It targets linear time-invariant systems subject to additive Gaussian disturbances and uses a probabilistic description of uncertainty to handle constraints.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method guarantee closed-loop satisfaction of probabilistic constraints?",{"text":80,"@type":76},"It uses a finitely determined maximal admissible set for probabilistic constraints and reconditions the predicted probabilistic constraints at every time step based on current knowledge.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the key benefit of optimizing feedback policies online compared with fixed-feedback approaches?",{"text":84,"@type":76},"Online optimization over disturbance feedback policies improves performance and reduces conservatism while maintaining recursive feasibility for the chance-constrained convex optimization problem.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":28,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]