{"department":[{"_id":"655"}],"type":"preprint","oa":"1","citation":{"short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, ArXiv:2312.10460 (2023).","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error analysis of kernel EDMD for prediction and control in the Koopman  framework,” <i>arXiv:2312.10460</i>. 2023.","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2023, title={Error analysis of kernel EDMD for prediction and control in the Koopman  framework}, journal={arXiv:2312.10460}, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2023} }","ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error analysis of kernel EDMD for prediction and control in the Koopman  framework. <i>arXiv:231210460</i>. Published online 2023.","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Analysis of Kernel EDMD for Prediction and Control in the Koopman  Framework.” <i>ArXiv:2312.10460</i>, 2023.","mla":"Philipp, Friedrich, et al. “Error Analysis of Kernel EDMD for Prediction and Control in the Koopman  Framework.” <i>ArXiv:2312.10460</i>, 2023.","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2023). Error analysis of kernel EDMD for prediction and control in the Koopman  framework. In <i>arXiv:2312.10460</i>."},"user_id":"47427","main_file_link":[{"url":"https://arxiv.org/pdf/2312.10460.pdf","open_access":"1"}],"author":[{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"first_name":"Manuel","last_name":"Schaller","full_name":"Schaller, Manuel"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"},{"orcid":"0000-0002-3389-793X","id":"47427","first_name":"Sebastian","full_name":"Peitz, Sebastian","last_name":"Peitz"},{"first_name":"Feliks","last_name":"Nüske","full_name":"Nüske, Feliks"}],"year":"2023","external_id":{"arxiv":["2312.10460"]},"date_created":"2024-02-06T08:49:50Z","status":"public","_id":"51158","abstract":[{"text":"Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to\r\napproximate the Koopman operator for deterministic and stochastic (control)\r\nsystems. This operator is linear and encompasses full information on the\r\n(expected stochastic) dynamics. In this paper, we analyze a kernel-based EDMD\r\nalgorithm, known as kEDMD, where the dictionary consists of the canonical\r\nkernel features at the data points. The latter are acquired by i.i.d. samples\r\nfrom a user-defined and application-driven distribution on a compact set. We\r\nprove bounds on the prediction error of the kEDMD estimator when sampling from\r\nthis (not necessarily ergodic) distribution. The error analysis is further\r\nextended to control-affine systems, where the considered invariance of the\r\nReproducing Kernel Hilbert Space is significantly less restrictive in\r\ncomparison to invariance assumptions on an a-priori chosen dictionary.","lang":"eng"}],"publication":"arXiv:2312.10460","title":"Error analysis of kernel EDMD for prediction and control in the Koopman  framework","date_updated":"2024-02-06T08:50:32Z","language":[{"iso":"eng"}]}