{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T04:37:34Z","timestamp":1780461454312,"version":"3.54.1"},"reference-count":48,"publisher":"Walter de Gruyter GmbH","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator representation of the nonlinear system, for which a bilinear surrogate model is estimated based on data. In contrast to existing Koopman-based estimation procedures, we state guaranteed bounds on the approximation error using the stability- and certificate-oriented extended dynamic mode decomposition (SafEDMD) framework. The resulting surrogate model and the uncertainty bounds allow us to design controllers via robust control theory and sum-of-squares optimization, guaranteeing desirable properties for the closed-loop system. We present results on stabilization both in discrete and continuous time, and we derive a method for controller design with performance objectives. The benefits of the presented framework over established approaches are demonstrated with a numerical example.<\/jats:p>","DOI":"10.1515\/auto-2024-0162","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T20:52:17Z","timestamp":1748638337000},"page":"413-428","source":"Crossref","is-referenced-by-count":9,"title":["Koopman-based control of nonlinear systems with closed-loop guarantees"],"prefix":"10.1515","volume":"73","author":[{"given":"Robin","family":"Str\u00e4sser","sequence":"first","affiliation":[{"name":"Institute for Systems Theory and Automatic Control, University of Stuttgart , 70550 Stuttgart , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julian","family":"Berberich","sequence":"additional","affiliation":[{"name":"Institute for Systems Theory and Automatic Control, University of Stuttgart , 70550 Stuttgart , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manuel","family":"Schaller","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics , Chemnitz University of Technology , 09111 Chemnitz , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karl","family":"Worthmann","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Technische Universit\u00e4t Ilmenau , 98693 Ilmenau , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frank","family":"Allg\u00f6wer","sequence":"additional","affiliation":[{"name":"Institute for Systems Theory and Automatic Control, University of Stuttgart , 70550 Stuttgart , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2025,5,28]]},"reference":[{"key":"2025053020521292397_j_auto-2024-0162_ref_001","doi-asserted-by":"crossref","unstructured":"Z.-S. Hou and Z. Wang, \u201cFrom model-based control to data-driven control: survey, classification and perspective,\u201d Inf. Sci., vol.\u00a0235, pp.\u00a03\u201335, 2013. https:\/\/doi.org\/10.1016\/j.ins.2012.07.014.","DOI":"10.1016\/j.ins.2012.07.014"},{"key":"2025053020521292397_j_auto-2024-0162_ref_002","doi-asserted-by":"crossref","unstructured":"I. Markovsky and F. D\u00f6rfler, \u201cBehavioral systems theory in data-driven analysis, signal processing, and control,\u201d Annu. Rev. Control, vol.\u00a052, pp.\u00a042\u201364, 2021. https:\/\/doi.org\/10.1016\/j.arcontrol.2021.09.005.","DOI":"10.1016\/j.arcontrol.2021.09.005"},{"key":"2025053020521292397_j_auto-2024-0162_ref_003","doi-asserted-by":"crossref","unstructured":"H. J. van Waarde, J. Eising, M. K. Camlibel, and H. L. Trentelman, \u201cThe informativity approach to data-driven analysis and control,\u201d IEEE Control Syst. Mag., vol.\u00a043, no.\u00a06, pp.\u00a032\u201366, 2023. https:\/\/doi.org\/10.1109\/mcs.2023.3310305.","DOI":"10.1109\/MCS.2023.3310305"},{"key":"2025053020521292397_j_auto-2024-0162_ref_004","doi-asserted-by":"crossref","unstructured":"T. Faulwasser, R. Ou, G. Pan, P. Schmitz, and K. Worthmann, \u201cBehavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again,\u201d Annu. Rev. Control, vol.\u00a055, pp.\u00a092\u2013117, 2023. https:\/\/doi.org\/10.1016\/j.arcontrol.2023.03.005.","DOI":"10.1016\/j.arcontrol.2023.03.005"},{"key":"2025053020521292397_j_auto-2024-0162_ref_005","doi-asserted-by":"crossref","unstructured":"J. Berberich and F. Allg\u00f6wer, \u201cAn overview of systems-theoretic guarantees in data-driven model predictive control,\u201d Annu. Rev. Control, Robot., Auton. 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Syst., vol.\u00a04, pp.\u00a059\u201387, 2021. https:\/\/doi.org\/10.1146\/annurev-control-071020-010108.","DOI":"10.1146\/annurev-control-071020-010108"},{"key":"2025053020521292397_j_auto-2024-0162_ref_011","doi-asserted-by":"crossref","unstructured":"A. Mauroy, I. Mezi\u0107, and Y. Susuki, The Koopman operator in systems and Control, Berlin, Springer, 2020.","DOI":"10.1007\/978-3-030-35713-9"},{"key":"2025053020521292397_j_auto-2024-0162_ref_012","doi-asserted-by":"crossref","unstructured":"P. Bevanda, S. Sosnowski, and S. Hirche, \u201cKoopman operator dynamical models: learning, analysis and control,\u201d Annu. Rev. Control, vol.\u00a052, pp.\u00a0197\u2013212, 2021. https:\/\/doi.org\/10.1016\/j.arcontrol.2021.09.002.","DOI":"10.1016\/j.arcontrol.2021.09.002"},{"key":"2025053020521292397_j_auto-2024-0162_ref_013","doi-asserted-by":"crossref","unstructured":"M. Korda and I. 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Syst., vol.\u00a021, no.\u00a08, pp.\u00a02431\u20132443, 2023. https:\/\/doi.org\/10.1007\/s12555-023-0193-1.","DOI":"10.1007\/s12555-023-0193-1"},{"key":"2025053020521292397_j_auto-2024-0162_ref_023","doi-asserted-by":"crossref","unstructured":"M. Budi\u0161i\u0107, R. Mohr, and I. Mezi\u0107, \u201cApplied Koopmanism,\u201d Chaos, vol.\u00a022, no.\u00a04, 2012, Art. no. 047510. https:\/\/doi.org\/10.1063\/1.4772195.","DOI":"10.1063\/1.4772195"},{"key":"2025053020521292397_j_auto-2024-0162_ref_024","doi-asserted-by":"crossref","unstructured":"Y. Chen and U. Vaidya, \u201cSample complexity for nonlinear stochastic dynamics,\u201d in Proc. IEEE American Control Conference (ACC), 2019, pp.\u00a03526\u20133531.","DOI":"10.23919\/ACC.2019.8815138"},{"key":"2025053020521292397_j_auto-2024-0162_ref_025","doi-asserted-by":"crossref","unstructured":"F. N\u00fcske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, \u201cFinite-data error bounds for Koopman-based prediction and control,\u201d J. Nonlinear Sci., vol.\u00a033, no.\u00a014, 2023, Art. no. 14. https:\/\/doi.org\/10.1007\/s00332-022-09862-1.","DOI":"10.1007\/s00332-022-09862-1"},{"key":"2025053020521292397_j_auto-2024-0162_ref_026","doi-asserted-by":"crossref","unstructured":"I. Mezi\u0107, \u201cOn numerical approximations of the Koopman operator,\u201d Mathematics, vol.\u00a010, no.\u00a07, p.\u00a01180, 2022. https:\/\/doi.org\/10.3390\/math10071180.","DOI":"10.3390\/math10071180"},{"key":"2025053020521292397_j_auto-2024-0162_ref_027","doi-asserted-by":"crossref","unstructured":"C. Zhang and E. Zuazua, \u201cA quantitative analysis of Koopman operator methods for system identification and predictions,\u201d C. R. Mec., vol.\u00a0351, no.\u00a0S1, pp.\u00a01\u201331, 2023. https:\/\/doi.org\/10.5802\/crmeca.138.","DOI":"10.5802\/crmeca.138"},{"key":"2025053020521292397_j_auto-2024-0162_ref_028","doi-asserted-by":"crossref","unstructured":"L. Bold, L. Gr\u00fcne, M. Schaller, and K. Worthmann, \u201cData-driven MPC with stability guarantees using extended dynamic mode decomposition,\u201d IEEE Trans. Autom. Control, vol.\u00a070, no.\u00a01, pp.\u00a0534\u2013541, 2025. https:\/\/doi.org\/10.1109\/tac.2024.3431169.","DOI":"10.1109\/TAC.2024.3431169"},{"key":"2025053020521292397_j_auto-2024-0162_ref_029","doi-asserted-by":"crossref","unstructured":"R. Str\u00e4sser, J. Berberich, and F. 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Olaru, \u201cControl design and analysis for discrete time bilinear systems using sum of squares methods,\u201d in Proc. 53rd IEEE Conference on Decision and Control (CDC), 2014, pp.\u00a03143\u20133148.","DOI":"10.1109\/CDC.2014.7039874"},{"key":"2025053020521292397_j_auto-2024-0162_ref_043","doi-asserted-by":"crossref","unstructured":"J. L\u00f6fberg, \u201cYALMIP: a toolbox for modeling and optimization in MATLAB,\u201d in Proc. IEEE International Conference on Robotics and Automation, 2004, pp.\u00a0284\u2013289.","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"2025053020521292397_j_auto-2024-0162_ref_044","doi-asserted-by":"crossref","unstructured":"J. L\u00f6fberg, \u201cPre- and post-processing sum-of-squares programs in practice,\u201d IEEE Trans. Autom. Control, vol.\u00a054, no.\u00a05, pp.\u00a01007\u20131011, 2009. https:\/\/doi.org\/10.1109\/tac.2009.2017144.","DOI":"10.1109\/TAC.2009.2017144"},{"key":"2025053020521292397_j_auto-2024-0162_ref_045","unstructured":"MOSEK ApS, The MOSEK Optimization Toolbox for MATLAB Manual. Version 9.3.21, 2022. Available at: https:\/\/docs.mosek.com\/latest\/faq\/faq.html#how-do-i-cite-mosek-in-an-academic-publication."},{"key":"2025053020521292397_j_auto-2024-0162_ref_046","doi-asserted-by":"crossref","unstructured":"S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. Nathan Kutz, \u201cKoopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,\u201d PLoS One, vol.\u00a011, no.\u00a02, pp.\u00a01\u201319, 2016. https:\/\/doi.org\/10.1371\/journal.pone.0150171.","DOI":"10.1371\/journal.pone.0150171"},{"key":"2025053020521292397_j_auto-2024-0162_ref_047","unstructured":"W. Tan, \u201cNonlinear control analysis and synthesis using sum-of-squares programming,\u201d Ph.D. dissertation, University of California, Berkeley, 2000."},{"key":"2025053020521292397_j_auto-2024-0162_ref_048","doi-asserted-by":"crossref","unstructured":"S. P. Boyd and L. 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