{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T04:37:56Z","timestamp":1775018276304,"version":"3.50.1"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T00:00:00Z","timestamp":1752624000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T00:00:00Z","timestamp":1752624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Carl-Zeiss-Stiftung,Germany","award":["n.a."],"award-info":[{"award-number":["n.a."]}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["n.a."],"award-info":[{"award-number":["n.a."]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016019","name":"Freistaat Th\u00fcringen","doi-asserted-by":"publisher","award":["n.a."],"award-info":[{"award-number":["n.a."]}],"id":[{"id":"10.13039\/100016019","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Deutsche Forschungsgemeinschaft,Germany","award":["WO 2056\/14-1"],"award-info":[{"award-number":["WO 2056\/14-1"]}]},{"DOI":"10.13039\/501100007826","name":"Technische Universit\u00e4t Ilmenau","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007826","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Extended dynamic mode decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected stochastic) dynamics. In this paper, we analyze kernel EDMD (kEDMD), where the dictionary consists of the canonical features at the data points. The latter are acquired by i.i.d. samples from a user-defined and application-driven distribution on a compact set. We prove bounds on the prediction error of the kEDMD estimator when sampling from this (not necessarily ergodic) distribution. The error analysis is further extended to control-affine systems, where the considered invariance of the reproducing kernel Hilbert space is significantly less restrictive in comparison to invariance assumptions on an a-priori chosen dictionary.<\/jats:p>","DOI":"10.1007\/s00332-025-10182-3","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T08:45:28Z","timestamp":1752655528000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Error Analysis of Kernel EDMD for Prediction and Control in the Koopman Framework"],"prefix":"10.1007","volume":"35","author":[{"given":"Friedrich M.","family":"Philipp","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Schaller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl","family":"Worthmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian","family":"Peitz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feliks","family":"N\u00fcske","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"key":"10182_CR1","series-title":"An Introduction to Nonlinear Analysis","doi-asserted-by":"crossref","DOI":"10.1515\/9783110853698","volume-title":"Ordinary Differential Equations","author":"H Amann","year":"1990","unstructured":"Amann, H.: Ordinary Differential Equations. An Introduction to Nonlinear Analysis, de Gruyter, Berlin, New York (1990)"},{"key":"10182_CR2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N Aronszajn","year":"1950","unstructured":"Aronszajn, N.: Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337\u2013404 (1950)","journal-title":"Trans. Am. Math. Soc."},{"key":"10182_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-00227-9","volume-title":"Analysis and Geometry of Markov DiffusGrundlehren der mathematischen Wissenschaftenion Operators","author":"D Bakry","year":"2014","unstructured":"Bakry, D., Gentil, I., Ledoux, M.: Analysis and Geometry of Markov DiffusGrundlehren der mathematischen Wissenschaftenion Operators. Springer, Cham (2014)"},{"key":"10182_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9096-9","volume-title":"Reproducing Kernel Hilbert Spaces in Probability and Statistics","author":"A Berlinet","year":"2004","unstructured":"Berlinet, A., Thomas-Agnan, C.: Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer Academic Publishers, New York (2004)"},{"key":"10182_CR5","unstructured":"Bevanda, P., Beier, M., Lederer, A., Sosnowski, S., H\u00fcllermeier, E., Hirche, S.: Koopman kernel regression. In: Proceedings of the 37th International Conference on Neural Information Processing Systems, article no. 713 (2024)"},{"key":"10182_CR6","doi-asserted-by":"crossref","unstructured":"Bold, L., Gr\u00fcne, L., Schaller, M., Worthmann, K.: Data-driven MPC with stability guarantees using extended dynamic mode decomposition. IEEE Trans. Autom. Control 70(1), 534\u2013541 (2025a)","DOI":"10.1109\/TAC.2024.3431169"},{"key":"10182_CR7","unstructured":"Bold, L., Philipp, F.M., Schaller, M., Worthmann, K.: Kernel-based Koopman approximants for control: flexible sampling, error analysis, and stability (2025b). Preprint arXiv:2412.02811"},{"issue":"2","key":"10182_CR8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1137\/21M1401243","volume":"64","author":"SL Brunton","year":"2022","unstructured":"Brunton, S.L., Budisic, M., Kaiser, E., Kutz, J.N.: Modern Koopman theory for dynamical systems. SIAM Rev. 64(2), 229\u2013340 (2022)","journal-title":"SIAM Rev."},{"key":"10182_CR9","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1109\/9.587345","volume":"42","author":"B Castillo","year":"1997","unstructured":"Castillo, B., Di Gennaro, S., Monaco, S., Normand-Cyrot, D.: On regulation under sampling. IEEE Trans. Autom. Control 42, 864\u2013868 (1997)","journal-title":"IEEE Trans. Autom. Control"},{"key":"10182_CR10","doi-asserted-by":"crossref","unstructured":"Chen, Y., Vaidya, U.: Sample complexity for non-linear stochastic systems. In: 2019 American Control Conference (ACC), Philadelphia, USA, July 10\u201312, pp. 3526\u20133531 (2019)","DOI":"10.23919\/ACC.2019.8815138"},{"issue":"5","key":"10182_CR11","doi-asserted-by":"crossref","first-page":"2979","DOI":"10.1137\/19M1265995","volume":"58","author":"J-M Coron","year":"2020","unstructured":"Coron, J.-M., Gr\u00fcne, L., Worthmann, K.: Model predictive control, cost controllability, and homogeneity. SIAM J. Control. Optim. 58(5), 2979\u20132996 (2020)","journal-title":"SIAM J. Control. Optim."},{"key":"10182_CR12","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511662829","volume-title":"Ergodicity for Infinite Dimensional Systems","author":"G Da Prato","year":"1996","unstructured":"Da Prato, G., Zabczyk, J.: Ergodicity for Infinite Dimensional Systems. London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1996)"},{"key":"10182_CR13","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.acha.2021.02.004","volume":"54","author":"S Das","year":"2021","unstructured":"Das, S., Giannakis, D., Slawinska, J.: Reproducing kernel Hilbert space compactification of unitary evolution groups. Appl. Comput. Harmon. Anal. 54, 75\u2013136 (2021)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"10182_CR14","doi-asserted-by":"crossref","DOI":"10.1201\/b18333","volume-title":"Measure Theory and Fine Properties of Functions","author":"LC Evans","year":"2015","unstructured":"Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (2015)"},{"key":"10182_CR15","unstructured":"Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators. Translations of Mathematical Monographs, vol. 18. American Mathematical Society, Providence (1969)"},{"key":"10182_CR16","unstructured":"Gonzalez, E., Abudia, M., Jury, M., Kamalapurkar, R., Rosenfeld, J.A.: The kernel perspective on dynamic mode decomposition (2023). Preprint arXiv:2106.00106"},{"issue":"6","key":"10182_CR17","doi-asserted-by":"crossref","first-page":"2715","DOI":"10.1109\/TAC.2021.3088802","volume":"67","author":"D Goswami","year":"2021","unstructured":"Goswami, D., Paley, D.A.: Bilinearization, reachability, and optimal control of control-affine nonlinear systems: a Koopman spectral approach. IEEE Trans. Autom. Control 67(6), 2715\u20132728 (2021)","journal-title":"IEEE Trans. Autom. Control"},{"key":"10182_CR18","doi-asserted-by":"crossref","unstructured":"Gr\u00fcne, L., Worthmann, K.: Sampled-data redesign for nonlinear multi-input systems. In: Geometric Control And Nonsmooth Analysis: In Honor of the 73rd Birthday of H. Hermes and of the 71st Birthday of R.T. Rockafellar, pp. 206\u2013227. World Scientific (2008)","DOI":"10.1142\/9789812776075_0011"},{"key":"10182_CR19","doi-asserted-by":"crossref","DOI":"10.1088\/2632-2153\/abf0f5","volume":"2","author":"E Kaiser","year":"2021","unstructured":"Kaiser, E., Kutz, J.N., Brunton, S.L.: Data-driven discovery of Koopman eigenfunctions for control. Mach. Learn. Sci. Technol. 2, 035023 (2021)","journal-title":"Mach. Learn. Sci. Technol."},{"key":"10182_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66282-9","volume-title":"Perturbation Theory for Linear Operators","author":"T Kato","year":"1995","unstructured":"Kato, T.: Perturbation Theory for Linear Operators. Springer, Berlin Heidelberg (1995)"},{"key":"10182_CR21","first-page":"51","volume":"1","author":"S Klus","year":"2016","unstructured":"Klus, S., Koltai, P., Sch\u00fctte, C.: On the numerical approximation of the Perron\u2013Frobenius and Koopman operator. J. Comput. Dyn. 1, 51\u201379 (2016)","journal-title":"J. Comput. Dyn."},{"issue":"3","key":"10182_CR22","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1007\/s00332-017-9437-7","volume":"28","author":"S Klus","year":"2018","unstructured":"Klus, S., N\u00fcske, F., Koltai, P., Wu, H., Kevrekidis, I., Sch\u00fctte, C., No\u00e9, F.: Data-driven model reduction and transfer operator approximation. J. Nonlinear Sci. 28(3), 985\u20131010 (2018)","journal-title":"J. Nonlinear Sci."},{"key":"10182_CR23","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s00332-019-09574-z","volume":"30","author":"S Klus","year":"2020","unstructured":"Klus, S., Schuster, I., Muandet, K.: Eigendecompositions of transfer operators in reproducing kernel Hilbert spaces. J. Nonlinear Sci. 30, 283\u2013315 (2020)","journal-title":"J. Nonlinear Sci."},{"key":"10182_CR24","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1137\/24M1650120","volume":"24","author":"F K\u00f6hne","year":"2024","unstructured":"K\u00f6hne, F., Philipp, F., Schaller, M., Schiela, A., Worthmann, K.: $$L^\\infty $$-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition. SIAM J. Appl. Dyn. Syst. 24, 501\u2013529 (2024)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"10182_CR25","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1073\/pnas.17.5.315","volume":"5","author":"BO Koopman","year":"1931","unstructured":"Koopman, B.O.: Hamiltonian systems and transformations in Hilbert space. Proc. Natl. Acad. Sci. 5, 315\u2013318 (1931)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"10182_CR26","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.automatica.2018.03.046","volume":"93","author":"M Korda","year":"2018","unstructured":"Korda, M., Mezi\u0107, I.: Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica 93, 149\u2013160 (2018)","journal-title":"Automatica"},{"key":"10182_CR27","first-page":"4017","volume":"35","author":"V Kostic","year":"2022","unstructured":"Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L., Pontil, M.: Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces. Adv. Neural. Inf. Process. Syst. 35, 4017\u20134031 (2022)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"10182_CR28","unstructured":"Kostic, V., Lounici, K., Novelli, P., Pontil, M.: Sharp spectral rates for Koopman operator learning. In: Proceedings of the 37th International Conference on Neural Information Processing Systems, article no. 1403 (2024)"},{"key":"10182_CR29","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s41478-019-00211-2","volume":"29","author":"V K\u00fchner","year":"2021","unstructured":"K\u00fchner, V.: What can Koopmanism do for attractors in dynamical systems? J. Anal. 29, 449\u2013471 (2021)","journal-title":"J. Anal."},{"key":"10182_CR30","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1017\/S0962492916000039","volume":"25","author":"T Leli\u00e8vre","year":"2016","unstructured":"Leli\u00e8vre, T., Stoltz, G.: Partial differential equations and stochastic methods in molecular dynamics. Acta Numer 25, 681\u2013880 (2016)","journal-title":"Acta Numer"},{"key":"10182_CR31","doi-asserted-by":"crossref","DOI":"10.1142\/p579","volume-title":"Free Energy Computations","author":"T Leli\u00e8vre","year":"2010","unstructured":"Leli\u00e8vre, T., Rousset, M., Stoltz, G.: Free Energy Computations. Impertial College Press, London (2010)"},{"issue":"7","key":"10182_CR32","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1002\/rnc.4053","volume":"28","author":"Z Li","year":"2018","unstructured":"Li, Z., Zhao, J.: Output feedback stabilization for a general class of nonlinear systems via sampled-data control. Int. J. Robust Nonlinear Control 28(7), 2853\u20132867 (2018)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"10182_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-35713-9","volume-title":"Koopman Operator in Systems and Control","author":"A Mauroy","year":"2020","unstructured":"Mauroy, A., Susuki, Y., Mezi\u0107, I.: Koopman Operator in Systems and Control. Springer, Berlin (2020)"},{"key":"10182_CR34","unstructured":"Mollenhauer, M.: on the Statistical Approximation of Conditional Expectation Operators. Dissertation, Freie Universit\u00e4t Berlin (2021)"},{"key":"10182_CR35","doi-asserted-by":"crossref","unstructured":"Ne\u0161i\u0107, D., Teel, A.R.: Sampled-data control of nonlinear systems: an overview of recent results. In: Moheimani, S.R. (ed.) Perspectives in Robust Control. Lecture Notes in Control and Information Sciences 268, pp. 221\u2013239. Springer, London (2007)","DOI":"10.1007\/BFb0110623"},{"issue":"7","key":"10182_CR36","doi-asserted-by":"crossref","DOI":"10.1063\/5.0162619","volume":"159","author":"F N\u00fcske","year":"2023","unstructured":"N\u00fcske, F., Klus, S.: Efficient approximation of molecular kinetics using random Fourier features. J. Chem. Phys. 159(7), 074105 (2023)","journal-title":"J. Chem. Phys."},{"key":"10182_CR37","doi-asserted-by":"crossref","first-page":"1739","DOI":"10.1021\/ct4009156","volume":"10","author":"F N\u00fcske","year":"2014","unstructured":"N\u00fcske, F., Keller, B.G., P\u00e9rez-Hern\u00e1ndez, G., Mey, A.S.J.S., No\u00e9, F.: Variational approach to molecular kinetics. J. Chem. Theory Comput. 10, 1739\u20131752 (2014)","journal-title":"J. Chem. Theory Comput."},{"key":"10182_CR38","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2021.133018","volume":"427","author":"F N\u00fcske","year":"2021","unstructured":"N\u00fcske, F., Gel\u00df, P., Klus, S., Clementi, C.: Tensor-based computation of metastable and coherent sets. Physica D 427, 133018 (2021)","journal-title":"Physica D"},{"key":"10182_CR39","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s00332-022-09862-1","volume":"33","author":"F N\u00fcske","year":"2023","unstructured":"N\u00fcske, F., Peitz, S., Philipp, F., Schaller, M., Worthmann, K.: Finite-data error bounds for Koopman-based prediction and control. J. Nonlinear Sci. 33, 14 (2023)","journal-title":"J. Nonlinear Sci."},{"key":"10182_CR40","unstructured":"\u00d8ksendal, B.: Stochastic Differential Equations. An Introduction with Applications, 5th edn. Springer, Heidelberg (2000)"},{"key":"10182_CR41","doi-asserted-by":"crossref","unstructured":"Paulsen, V.I., Raghupathi, M.: An Introduction to the Theory of Reproducing Kernel Hilbert Spaces. Cambridge Studies in Advanced Mathematics 152, Cambridge University Press, Cambridge (2016)","DOI":"10.1017\/CBO9781316219232"},{"issue":"3","key":"10182_CR42","doi-asserted-by":"crossref","first-page":"2162","DOI":"10.1137\/20M1325678","volume":"19","author":"S Peitz","year":"2020","unstructured":"Peitz, S., Otto, S.E., Rowley, C.W.: Data-driven model predictive control using interpolated Koopman generators. SIAM J. Appl. Dyn. Syst. 19(3), 2162\u20132193 (2020)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"10182_CR43","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.jmaa.2016.11.009","volume":"448","author":"F Philipp","year":"2017","unstructured":"Philipp, F.: Bessel orbits of normal operators. J. Math. Anal. Appl. 448, 767\u2013785 (2017)","journal-title":"J. Math. Anal. Appl."},{"key":"10182_CR44","doi-asserted-by":"crossref","DOI":"10.1016\/j.acha.2024.101657","volume":"71","author":"F Philipp","year":"2024","unstructured":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., N\u00fcske, F.: Error bounds for kernel-based approximations of the Koopman operator. Appl. Comput. Harmon. Anal. 71, 101657 (2024)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"10182_CR45","doi-asserted-by":"crossref","first-page":"1679","DOI":"10.1214\/aop\/1176988477","volume":"22","author":"I Pinelis","year":"1994","unstructured":"Pinelis, I.: Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22, 1679\u20131706 (1994)","journal-title":"Ann. Probab."},{"key":"10182_CR46","unstructured":"Rahimi, A., Recht, B.: Random features for large-scale kernel machines. In: Advances in Neural Information Processing Systems, vol. 20 (2007)"},{"key":"10182_CR47","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3206.001.0001","volume-title":"Gaussian Processes for Machine Learning","author":"CE Rasmussen","year":"2005","unstructured":"Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2005)"},{"key":"10182_CR48","volume-title":"Functional Analysis","author":"F Riesz","year":"1955","unstructured":"Riesz, F., Nagy, B.: Functional Analysis. Blackie & Son Ltd., Glasgow (1955)"},{"key":"10182_CR49","series-title":"Springer Texts in Statistics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4145-2","volume-title":"Monte Carlo Statistical Methods","author":"CP Robert","year":"2004","unstructured":"Robert, C.P., Casella, G.: Monte Carlo Statistical Methods. Springer Texts in Statistics, Springer, Berlin (2004)"},{"key":"10182_CR50","volume-title":"Real and Complex Analysis","author":"W Rudin","year":"1987","unstructured":"Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill Inc., New York (1987)","edition":"3"},{"key":"10182_CR51","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.ifacol.2023.02.029","volume":"56","author":"M Schaller","year":"2023","unstructured":"Schaller, M., Worthmann, K., Philipp, F., Peitz, S., N\u00fcske, F.: Towards reliable data-based optimal and predictive control using extended DMD. IFAC-PapersOnLine 56, 169\u2013174 (2023)","journal-title":"IFAC-PapersOnLine"},{"key":"10182_CR52","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1017\/S0022112010001217","volume":"656","author":"PJ Schmid","year":"2010","unstructured":"Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5\u201328 (2010)","journal-title":"J. Fluid Mech."},{"key":"10182_CR53","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-77242-4","volume-title":"Support Vector Machines","author":"I Steinwart","year":"2008","unstructured":"Steinwart, I., Christmann, A.: Support Vector Machines. Springer, Berlin (2008)"},{"key":"10182_CR54","doi-asserted-by":"crossref","first-page":"4635","DOI":"10.1109\/TIT.2006.881713","volume":"52","author":"I Steinwart","year":"2006","unstructured":"Steinwart, I., Hush, D., Scovel, C.: An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels. IEEE Trans. Inf. Theory 52, 4635\u20134643 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10182_CR55","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1016\/j.ifacol.2023.10.1190","volume":"56","author":"R Str\u00e4sser","year":"2023","unstructured":"Str\u00e4sser, R., Berberich, J., Allg\u00f6wer, F.: Robust data-driven control for nonlinear systems using the Koopman operator. IFAC-PapersOnLine 56, 2257\u20132262 (2023)","journal-title":"IFAC-PapersOnLine"},{"issue":"1","key":"10182_CR56","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/TAC.2024.3425770","volume":"70","author":"R Str\u00e4sser","year":"2025","unstructured":"Str\u00e4sser, R., Schaller, M., Worthmann, K., Berberich, J., Allg\u00f6wer, F.: Koopman-based feedback design with stability guarantees. IEEE Trans. Autom. Control 70(1), 355\u2013370 (2025)","journal-title":"IEEE Trans. Autom. Control"},{"key":"10182_CR57","doi-asserted-by":"crossref","unstructured":"Surana, A.: Koopman operator based observer synthesis for control-affine nonlinear systems. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 6492\u20136499. IEEE (2016)","DOI":"10.1109\/CDC.2016.7799268"},{"key":"10182_CR58","doi-asserted-by":"crossref","unstructured":"van Goor, P., Mahony, R., Schaller, M., Worthmann, K.: Reprojection methods for Koopman-based modelling and prediction. In: 2023 62nd IEEE Conference on Decision and Control (CDC), Singapore, Singapore, pp. 315\u2013321 (2023)","DOI":"10.1109\/CDC49753.2023.10383796"},{"key":"10182_CR59","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0601-9","volume-title":"Ordinary Differential Equations","author":"W Walter","year":"1998","unstructured":"Walter, W.: Ordinary Differential Equations. Springer, Berlin (1998)"},{"key":"10182_CR60","doi-asserted-by":"crossref","unstructured":"Williams, M.O., Kevrekidis, I.G., Rowley, C.W.: A data-driven approximation of the Koopman operator: extending dynamic mode decomposition. J. Nonlinear Sci. 25, 1307\u20131346 (2015a)","DOI":"10.1007\/s00332-015-9258-5"},{"key":"10182_CR61","doi-asserted-by":"crossref","unstructured":"Williams, M.O., Rowley, C.W., Kevrekidis, I.: A kernel-based method for data-driven Koopman spectral analysis. J. Comput. Dyn. 2(2), 247\u2013265 (2015b)","DOI":"10.3934\/jcd.2015005"},{"issue":"18","key":"10182_CR62","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/j.ifacol.2016.10.248","volume":"49","author":"MO Williams","year":"2016","unstructured":"Williams, M.O., Hemati, M.S., Dawson, S., Kevrekidis, I.G., Rowley, C.W.: Extending data-driven Koopman analysis to actuated systems. IFAC-PapersOnLine 49(18), 704\u2013709 (2016)","journal-title":"IFAC-PapersOnLine"},{"issue":"1","key":"10182_CR63","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1137\/12086652X","volume":"52","author":"K Worthmann","year":"2014","unstructured":"Worthmann, K., Reble, M., Gr\u00fcne, L., Allg\u00f6wer, F.: The role of sampling for stability and performance in unconstrained nonlinear model predictive control. SIAM J. Control. Optim. 52(1), 581\u2013605 (2014)","journal-title":"SIAM J. Control. Optim."},{"key":"10182_CR64","first-page":"1","volume":"35","author":"C Zhang","year":"2023","unstructured":"Zhang, C., Zuazua, E.: A quantitative analysis of Koopman operator methods for system identification and predictions. C. R. M\u00e9c. 35, 1\u201331 (2023)","journal-title":"C. R. M\u00e9c."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-025-10182-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-025-10182-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-025-10182-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T16:58:00Z","timestamp":1757523480000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-025-10182-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,16]]},"references-count":64,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["10182"],"URL":"https:\/\/doi.org\/10.1007\/s00332-025-10182-3","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,16]]},"assertion":[{"value":"17 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"92"}}