[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83690-en":3,"doc-seo-83690-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83690,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Data-driven Kernel-based Predictive Control with Stability and Robustness Guarantees","Data-driven kernel-based predictive control (DDKPC) is analyzed through closed-loop theory built solely from input-output data. A robust predictive control formulation couples with a multi-step kernel predictor that implicitly represents nonlinear dynamics via the representer theorem. For noise-free data, recursive feasibility and closed-loop stability are guaranteed when the prediction horizon is long enough and kernel representation error is small. Computational load is reduced using penalty relaxation, and robustness to measurement noise is obtained by unifying representation mismatch and bounded noise into a single uncertainty bound. The method is extended to slowly time-varying nonlinear systems via periodic kernel predictor reconstruction using a fixed-budget online dictionary managed by ALD. Numerical examples validate the approach.","Data-driven Kernel-based Predictive Control with Stability  \nand Robustness Guarantees  \nWenjie Liu, Yifei Li, Gang Wang, Senior Member, IEEE, and Lihua Xie, Fellow, IEEE  \narXiv :2607 .02851v1 [ ee ss . SY] 3 Jul 2026  \nAbstract—In this paper, we provide a theoretical analysis of the closed-loop properties of a data-driven kernel-based predictive control (DDKPC) scheme developed solely from input-output data. The proposed formulation integrates a robust data-driven predictive control framework with a multi-step predictor for nonlinear systems constructed via kernel-based methods. This predictor implicitly captures the system’s nonlinear behavior using the representer theorem. For the nominal case with noise-free data, we prove that the DDKPC scheme guarantees recursive feasibility and closed-loop stability, provided that the prediction horizon is sufficiently long and the kernel representation error is sufficiently small. To facilitate real-time implementation, we introduce a penalty relaxation formulation to alleviate the computational burden inherently caused by nonconvex implicit constraints. Furthermore, the framework is robustified against measurement noise by aggregating the representation mismatch and the bounded noise into a unified uncertainty bound. Finally, we extend the DDKPC framework to slowly time-varying nonlinear systems by periodically reconstructing the kernel predictor from a fixedbudget online dictionary managed by the approximate linear dependency (ALD) criterion. Under suitable conditions on the rate of variation of the input-output evolution and the online prediction error, recursive feasibility and practical closed-loop stability are preserved. The effectiveness of the proposed approach is illustrated through numerical examples.  \nIndex terms—Data-driven control, nonlinear control, kernelbased representation, predictive control  \nI. INTRODUCTION  \nModel predictive control (MPC) is widely used because it systematically computes control actions through online optimization while handling nonlinear dynamics, constraints, and closed-loop performance requirements [1], [2] . However, its effectiveness relies on an accurate predictive model, whose construction can be costly or infeasible for systems with high dimensionality, complex couplings, and significant unmodeled effects. This modeling burden remains a key obstacle to broader MPC deployment.  \nThe increasing volume of data available from modern systems, combined with advances in computation, has motivated a shift toward data-driven predictive control frameworks that reduce or eliminate explicit model identification. For linear timeinvariant (LTI) systems, Willems et al’s fundamental lemma [3] provides a direct data-based parametrization of admissible trajectories, which leads to recent advancement in data-driven  \nThis work was supported by the Ministry of Education, Singapore, under AcRF Tier 1 Grant RG64/23, and in part by the National Natural Science Foundation of China under Grant U23B2059 .  \nWenjie Liu, Yifei Li, and Lihua Xie are with the Centre for Advanced Robotics Technology Innovation (CARTIN), School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore (e-mail: (wenjie.liu, li.yifei, elhxie)@[ntu.edu.sg](ntu.edu.sg)). Gang Wang is with the State Key Lab of Autonomous Intelligent Unmanned Systems and the School of Automation, Beijing Institute of Technology, Beijing 100081, China (email: [gangwang@bit.edu.cn](gangwang@bit.edu.cn)).  \ncontrol [4]–[9] . In this category, data-driven predictive control (DDPC) frameworks have shown that stabilizing recedinghorizon controllers can be synthesized purely from inputoutput data, even in settings involving disturbances and measurement noise [10]–[13], and network-induced issues [14]–[16] . However, these results lie in the category of LTI systems, while many emerging engineering systems operate in regimes where nonlinear effects are intrinsic and cannot be neglected.  \n","cbCaifV1LNjJ8DQX","https://ap.wps.com/l/cbCaifV1LNjJ8DQX","pdf",6575254,4,1,16,"English","en",105,"# Introduction\n## Model predictive control and data-driven predictive control\n## Extending data-driven predictive control to nonlinear systems\n## Proposed contribution and framework overview","[{\"question\":\"What is DDKPC and how is it constructed in the paper?\",\"answer\":\"The paper presents a data-driven kernel-based predictive control (DDKPC) scheme built solely from historical input-output data. It uses a multi-step implicit kernel predictor constructed through the representer theorem to capture nonlinear behavior.\"},{\"question\":\"What guarantees are proven for the nominal (noise-free) case?\",\"answer\":\"With noise-free data, the paper proves recursive feasibility and closed-loop stability. The results hold when the prediction horizon is sufficiently long and the kernel representation error is sufficiently small.\"},{\"question\":\"How does the method handle computation and measurement noise in practice?\",\"answer\":\"To reduce computational burden from nonconvex implicit constraints, the paper introduces a penalty relaxation formulation enabling efficient first-order optimization. For robustness, it aggregates representation mismatch and bounded measurement noise into a unified uncertainty bound.\"}]",1784189752,40,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"data-driven-kernel-based-predictive-control-with-stability-and-robustness-guarantees","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/data-driven-kernel-based-predictive-control-with-stability-and-robustness-guarantees/83690/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","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 is DDKPC and how is it constructed in the paper?","Question",{"text":75,"@type":76},"The paper presents a data-driven kernel-based predictive control (DDKPC) scheme built solely from historical input-output data. It uses a multi-step implicit kernel predictor constructed through the representer theorem to capture nonlinear behavior.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What guarantees are proven for the nominal (noise-free) case?",{"text":80,"@type":76},"With noise-free data, the paper proves recursive feasibility and closed-loop stability. The results hold when the prediction horizon is sufficiently long and the kernel representation error is sufficiently small.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method handle computation and measurement noise in practice?",{"text":84,"@type":76},"To reduce computational burden from nonconvex implicit constraints, the paper introduces a penalty relaxation formulation enabling efficient first-order optimization. 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