{"type":"preprint","publication":"arXiv:1801.06419","citation":{"ama":"Peitz S. Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data. <i>arXiv:180106419</i>. 2018.","chicago":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations  Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.","apa":"Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data. <i>ArXiv:1801.06419</i>.","bibtex":"@article{Peitz_2018, title={Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data}, journal={arXiv:1801.06419}, author={Peitz, Sebastian}, year={2018} }","ieee":"S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data,” <i>arXiv:1801.06419</i>. 2018.","mla":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations  Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.","short":"S. Peitz, ArXiv:1801.06419 (2018)."},"_id":"16292","department":[{"_id":"101"}],"title":"Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data","author":[{"last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}],"date_created":"2020-03-13T12:43:14Z","status":"public","abstract":[{"text":"In a recent article, we presented a framework to control nonlinear partial\r\ndifferential equations (PDEs) by means of Koopman operator based reduced models\r\nand concepts from switched systems. The main idea was to transform a control\r\nsystem into a set of autonomous systems for which the optimal switching\r\nsequence has to be computed. These individual systems can be approximated very\r\nefficiently by reduced order models obtained from data, and one can guarantee\r\nequality of the full and the reduced objective function under certain\r\nassumptions. In this article, we extend these results to continuous control\r\ninputs using convex combinations of multiple Koopman operators corresponding to\r\nconstant controls, which results in a bilinear control system. Although\r\nequality of the objectives can be carried over when the PDE depends linearly on\r\nthe control, we show that this approach is also valid in other scenarios using\r\nseveral flow control examples of varying complexity.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/1801.06419.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"user_id":"47427","year":"2018","date_updated":"2022-01-06T06:52:48Z","oa":"1"}