{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:26:38Z","timestamp":1777454798485,"version":"3.51.4"},"reference-count":36,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:00:00Z","timestamp":1773964800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Dutch Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Automatica"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.automatica.2026.112926","type":"journal-article","created":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T07:46:26Z","timestamp":1774251986000},"page":"112926","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Data-efficient global extremum seeking framework for constrained optimization of nonlinear dynamical systems"],"prefix":"10.1016","volume":"188","author":[{"given":"Wouter","family":"Weekers","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Saccon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathan","family":"van de Wouw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.automatica.2026.112926_b1","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s10898-004-9972-2","article-title":"A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems","volume":"31","author":"Ali","year":"2005","journal-title":"Journal of Global Optimization"},{"key":"10.1016\/j.automatica.2026.112926_b2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","article-title":"Theory of reproducing kernels","volume":"68","author":"Aronszajn","year":"1950","journal-title":"Transactions of the American Mathematical Society"},{"key":"10.1016\/j.automatica.2026.112926_b3","series-title":"2019 IEEE 58th conference on decision and control","first-page":"1494","article-title":"A geometric phasor extremum seeking control approach with measured constraints","author":"Atta","year":"2019"},{"key":"10.1016\/j.automatica.2026.112926_b4","series-title":"Optimization and Nonsmooth Analysis","author":"Clarke","year":"1990"},{"key":"10.1016\/j.automatica.2026.112926_b5","series-title":"Nonsmooth optimization and related topics","first-page":"89","article-title":"Exact penalty functions for nondifferentiable programming problems","author":"Di Pillo","year":"1989"},{"key":"10.1016\/j.automatica.2026.112926_b6","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1137\/0327068","article-title":"Exact penalty functions in constrained optimization","volume":"27","author":"Di Pillo","year":"1989","journal-title":"SIAM Journal on Control and Optimization"},{"key":"10.1016\/j.automatica.2026.112926_b7","series-title":"Research and codes","author":"Finkel","year":"2004"},{"key":"10.1016\/j.automatica.2026.112926_b8","series-title":"2024 32nd mediterranean conference on control and automation","first-page":"131","article-title":"Generalized saddle points seeking algorithms for convex optimization problems","author":"Grushkovskaya","year":"2024"},{"key":"10.1016\/j.automatica.2026.112926_b9","doi-asserted-by":"crossref","first-page":"3132","DOI":"10.1002\/rnc.3254","article-title":"A constrained extremum-seeking control approach","volume":"25","author":"Guay","year":"2015","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"10.1016\/j.automatica.2026.112926_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110415","article-title":"Sampled-data extremum-seeking framework for constrained optimization of nonlinear dynamical systems","volume":"142","author":"Hazeleger","year":"2022","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b11","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF00941892","article-title":"Lipschitzian optimization without the Lipschitz constant","volume":"79","author":"Jones","year":"1993","journal-title":"Journal of Optimization Theory and Applications"},{"key":"10.1016\/j.automatica.2026.112926_b12","doi-asserted-by":"crossref","first-page":"1970","DOI":"10.1016\/j.automatica.2013.04.006","article-title":"Multidimensional global extremum seeking via the DIRECT optimisation algorithm","volume":"49","author":"Khong","year":"2013","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b13","doi-asserted-by":"crossref","first-page":"2720","DOI":"10.1016\/j.automatica.2013.06.020","article-title":"Unified frameworks for sampled-data extremum seeking control: Global optimisation and multi-unit systems","volume":"49","author":"Khong","year":"2013","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b14","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/S0005-1098(99)00183-1","article-title":"Stability of extremum seeking feedback for general nonlinear dynamic systems","volume":"36","author":"Krsti\u0107","year":"2000","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b15","series-title":"IEEE conference on decision and control and European control conference","first-page":"4448","article-title":"Interconnection conditions for the stability of nonlinear sampled-data extremum seeking schemes","author":"Kvaternik","year":"2011"},{"key":"10.1016\/j.automatica.2026.112926_b16","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.ifacol.2019.12.043","article-title":"Constrained extremum seeking: A modified-barrier function approach","volume":"52","author":"Labar","year":"2019","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.automatica.2026.112926_b17","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2019.108496","article-title":"Constrained extremum seeking of a MIMO dynamic system","volume":"108","author":"Liao","year":"2019","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b18","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF00938542","article-title":"An algorithm for global optimization of Lipschitz continuous functions","volume":"57","author":"Meewella","year":"1988","journal-title":"Journal of Optimization Theory and Applications"},{"key":"10.1016\/j.automatica.2026.112926_b19","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/BF01580583","article-title":"An algorithm for finding the global maximum of a multimodal, multivariate function","volume":"34","author":"Mladineo","year":"1986","journal-title":"Mathematical Programming"},{"key":"10.1016\/j.automatica.2026.112926_b20","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/j.automatica.2012.12.004","article-title":"A non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm","volume":"49","author":"Ne\u0161i\u0107","year":"2013","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b21","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0041-5553(72)90115-2","article-title":"An algorithm for finding the absolute extremum of a function","volume":"12","author":"Piyavskii","year":"1972","journal-title":"USSR Computational Mathematics and Mathematical Physics"},{"key":"10.1016\/j.automatica.2026.112926_b22","doi-asserted-by":"crossref","first-page":"4949","DOI":"10.1109\/TAC.2017.2674519","article-title":"A robust event-triggered approach for fast sampled-data extremization and learning","volume":"62","author":"Poveda","year":"2017","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112926_b23","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.ifacol.2022.07.370","article-title":"Event-triggered extremum seeking control","volume":"55","author":"Rodrigues","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.automatica.2026.112926_b24","doi-asserted-by":"crossref","first-page":"10307","DOI":"10.1016\/j.ifacol.2023.10.950","article-title":"Dynamic event-triggered extremum seeking feedback","volume":"56","author":"Rodrigues","year":"2023","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.automatica.2026.112926_b25","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1109\/TAC.2022.3227907","article-title":"Robust uncertainty bounds in reproducing kernel Hilbert spaces: A convex optimization approach","volume":"68","author":"Scharnhorst","year":"2023","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112926_b26","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2023.111481","article-title":"100 Years of extremum seeking: A survey","volume":"161","author":"Scheinker","year":"2024","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b27","series-title":"Computational learning theory","first-page":"416","article-title":"A generalized representer theorem","author":"Sch\u00f6lkopf","year":"2001"},{"key":"10.1016\/j.automatica.2026.112926_b28","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1137\/0709036","article-title":"A sequential method seeking the global maximum of a function","volume":"9","author":"Shubert","year":"1972","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/j.automatica.2026.112926_b29","series-title":"Global Optimization with Non-Convex Constraints","author":"Strongin","year":"2000"},{"key":"10.1016\/j.automatica.2026.112926_b30","series-title":"Proceedings of the 29th Chinese control conference","first-page":"14","article-title":"Extremum seeking from 1922 to 2010","author":"Tan","year":"2010"},{"key":"10.1016\/j.automatica.2026.112926_b31","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.automatica.2006.01.014","article-title":"On non-local stability properties of extremum seeking control","volume":"42","author":"Tan","year":"2006","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112926_b32","series-title":"Proceedings of the 2001 American control conference","first-page":"2394","article-title":"Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming","author":"Teel","year":"2001"},{"key":"10.1016\/j.automatica.2026.112926_b33","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.conengprac.2019.03.008","article-title":"Constrained multivariable extremum-seeking for online fuel-efficiency optimization of diesel engines","volume":"87","author":"Van der Weijst","year":"2019","journal-title":"Control Engineering Practice"},{"key":"10.1016\/j.automatica.2026.112926_b34","doi-asserted-by":"crossref","first-page":"5317","DOI":"10.1109\/TAC.2022.3218944","article-title":"Kernel-based models for system analysis","volume":"68","author":"Van\u00a0Waarde","year":"2023","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112926_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2025.112506","article-title":"Data-efficient extremum-seeking control using kernel-based function approximation","volume":"181","author":"Weekers","year":"2025","journal-title":"Automatica"},{"issue":"3","key":"10.1016\/j.automatica.2026.112926_b36","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1109\/TAC.2024.3469785","article-title":"Semiglobal safety-filtered extremum seeking with unknown CBFs","volume":"70","author":"Williams","year":"2025","journal-title":"IEEE Transactions on Automatic Control"}],"container-title":["Automatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S000510982600110X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S000510982600110X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:57:33Z","timestamp":1777381053000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S000510982600110X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":36,"alternative-id":["S000510982600110X"],"URL":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112926","relation":{},"ISSN":["0005-1098"],"issn-type":[{"value":"0005-1098","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Data-efficient global extremum seeking framework for constrained optimization of nonlinear dynamical systems","name":"articletitle","label":"Article Title"},{"value":"Automatica","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112926","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"112926"}}