[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82243-en":3,"doc-seo-82243-105":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},82243,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Data-driven Predictive Control of Nonlinear Systems Using Weighted Regularization","Data-driven predictive control methods such as DeePC often rely on linear superposition, which enables global system inference from locally collected data via Willems’ fundamental lemma. That premise fails for nonlinear dynamics that change across operating regions. A weighted regularization framework is introduced that prioritizes data columns according to their distance to the current operating point, localizing the predictor while retaining the full dataset. The resulting optimization is shown well-posed, and experiments on a nonlinear two-tank system match or outperform hard selection schemes while preserving data rank and feasibility.","Data-driven predictive control of nonlinear systems  \nusing weighted regularization  \nFritz A. Engeln∗ , Sebastian Zieglmeier†, Marta Zagrowska∗ and Jan-Willem van Wingerden∗  \n∗ Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands  \n(email: {f.a.engeln,m.a.zagorowska,[j.w.vanwingerden](j.w.vanwingerden}@tudelft.nl)[}](j.w.vanwingerden}@tudelft.nl)[@tudelft.nl](j.w.vanwingerden}@tudelft.nl))  \n†Department of Technology Systems, University of Oslo, Kjeller, Norway (email: sebastiz@uio.no)  \narXiv :2607 .09187v1 [ ee ss . SY] 10 Jul 2026  \nAbstract—Data-driven control methods, like Data-enabled Predictive Control (DeePC), are often formulated for linear systems, where the principle of superposition allows global system behavior to be inferred from locally collected data through Willems’fundamental lemma. This principle does not hold for nonlinear systems, whose dynamics may vary across operating regions. We propose a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data. We show how the proposed weighting scheme induces operating point-dependent data prioritization and ensures a well-posed optimization problem. A numerical study on a nonlinear two-tank system demonstrates that the proposed method matches or outperforms hard data-selection schemes while retaining the full data matrix and its rank, thereby guaranteeing feasibility.  \nIndex Terms—data-driven control, nonlinear systems, weighted regularization, predictive control, data selection  \nI. INTRODUCTION  \nClassical predictive control methods such as model predictive control [1] rely on an accurate model of the system, obtained either from first-principles modeling or system identification [2] . More recently, increasing attention has been directed toward deriving control policies directly from data, thereby avoiding the need for an explicit parametric model of the system. Instead, Willems’fundamental lemma [3] is used to characterize the behavior of an unknown linear time-invariant (LTI) system by the linear subspace in which all input-output trajectories reside. Leveraging the fundamental lemma, datadriven predictive control (DPC) schemes can be formulated, such as data-enabled predictive control (DeePC) [4] .  \nSince the fundamental lemma presumes a noise-free LTI system, DeePC inherits these limitations. Introducing regularization relaxes the strict consistency requirement and lets DeePC tolerate measurement noise and mild nonlinearities, while also providing closed-loop stability and robustness guarantees [5] . When the system exhibits nonlinear behavior that cannot be well approximated by a single global linear model, controller performance deteriorates because trajectories  \nThis work is part of Hollandse Kust Noord wind farm innovation program where CrossWind C.V., Shell, Eneco, Grow and Siemens Gamesa are teaming up; funding for the PhD’s and PostDocs was provided by CrossWind C.V. and Siemens Gamesa.  \nThe code to reproduce the results of this paper is available at: [https://github](https://github). com/fengeln/weightDPC  \nrecorded in one operating region carry little information about the local behavior in another, causing both prediction accuracy and closed-loop performance to degrade [6] .  \nA recent and effective remedy is to localize the data online. Select-DPC, introduced in [7], retains at each time step only the columns of the data matrix that are closest to the current operating point according to either a norm- or a manifoldbased metric. This approach implicitly linearizes the dynamics in the trajectory space while preserving the convexity of the optimal control problem (OCP) and allowing the standard DeePC formulation to be reused. A closely related approach was independently proposed in [8] . Both methods","cbCaig5lO0ZIkA6d","https://ap.wps.com/l/cbCaig5lO0ZIkA6d","pdf",791458,1,7,"English","en",105,"# Introduction\n## Background: DeePC and limitations\n## Local data selection and its drawbacks\n## Proposed approach: weight-DPC\n## Contributions and validation","[{\"question\":\"Why does DeePC face difficulties for nonlinear systems?\",\"answer\":\"DeePC inherits limitations from Willems’ fundamental lemma, which assumes noise-free LTI behavior. For nonlinear dynamics, trajectories collected in one operating region may not represent local behavior elsewhere, degrading prediction and closed-loop performance.\"},{\"question\":\"What is the core idea behind weight-DPC?\",\"answer\":\"weight-DPC keeps the full data matrix but introduces distance-based weights in the regularization term. Data columns closer to the current operating point contribute more strongly to prediction, while distant columns are penalized.\"},{\"question\":\"What theoretical and experimental results are claimed for the method?\",\"answer\":\"The paper establishes well-posedness for ℓ2 and weighted ℓ2 regularization, including recursive feasibility and uniqueness, and shows that non-uniform weighting enables local data prioritization. A numerical study on a nonlinear two-tank system demonstrates performance comparable to or better than hard data-selection schemes while retaining full data rank and ensuring feasibility.\"}]",1784179094,18,{"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},"data-driven-predictive-control-of-nonlinear-systems-using-weighted-regularization","",{"@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/data-driven-predictive-control-of-nonlinear-systems-using-weighted-regularization/82243/",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},"Why does DeePC face difficulties for nonlinear systems?","Question",{"text":75,"@type":76},"DeePC inherits limitations from Willems’ fundamental lemma, which assumes noise-free LTI behavior. For nonlinear dynamics, trajectories collected in one operating region may not represent local behavior elsewhere, degrading prediction and closed-loop performance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core idea behind weight-DPC?",{"text":80,"@type":76},"weight-DPC keeps the full data matrix but introduces distance-based weights in the regularization term. Data columns closer to the current operating point contribute more strongly to prediction, while distant columns are penalized.",{"name":82,"@type":73,"acceptedAnswer":83},"What theoretical and experimental results are claimed for the method?",{"text":84,"@type":76},"The paper establishes well-posedness for ℓ2 and weighted ℓ2 regularization, including recursive feasibility and uniqueness, and shows that non-uniform weighting enables local data prioritization. A numerical study on a nonlinear two-tank system demonstrates performance comparable to or better than hard data-selection schemes while retaining full data rank and ensuring feasibility.","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":21,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},"Healthcare",40,"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"]