{"page":"2162-2193","date_updated":"2022-01-06T06:52:48Z","type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems","doi":"10.1137/20M1325678","issue":"3","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://epubs.siam.org/doi/pdf/10.1137/20M1325678"}],"user_id":"47427","citation":{"ieee":"S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control using Interpolated Koopman  Generators,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, pp. 2162–2193, 2020.","mla":"Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, 2020, pp. 2162–93, doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>.","ama":"Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>. 2020;19(3):2162-2193. doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>","bibtex":"@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control using Interpolated Koopman  Generators}, volume={19}, DOI={<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz, Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193} }","chicago":"Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i> 19, no. 3 (2020): 2162–93. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>.","apa":"Peitz, S., Otto, S. E., &#38; Rowley, C. W. (2020). Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>19</i>(3), 2162–2193. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>","short":"S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems 19 (2020) 2162–2193."},"date_created":"2020-03-17T09:53:01Z","_id":"16309","title":"Data-Driven Model Predictive Control using Interpolated Koopman  Generators","department":[{"_id":"101"}],"volume":19,"abstract":[{"lang":"eng","text":"In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis has also fueled the development of Koopman operator-based control\r\nframeworks. In order to preserve the relatively low data requirements for an\r\napproximation via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical systems can be realized by means of switched systems\r\ntechniques, using only a finite set of autonomous Koopman operator-based\r\nreduced models. These individual systems can be approximated very efficiently\r\nfrom data. The main idea is to transform a control system into a set of\r\nautonomous systems for which the optimal switching sequence has to be computed.\r\nIn this article, we extend these results to continuous control inputs using\r\nrelaxation. This way, we combine the advantages of the data efficiency of\r\napproximating a finite set of autonomous systems with continuous controls. We\r\nshow that when using the Koopman generator, this relaxation --- realized by\r\nlinear interpolation between two operators --- does not introduce any error for\r\ncontrol affine systems. This allows us to control high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate models. The efficiency of the\r\nproposed approach is demonstrated using several examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic fluidic pinball."}],"author":[{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"},{"first_name":"Samuel E.","full_name":"Otto, Samuel E.","last_name":"Otto"},{"first_name":"Clarence W.","last_name":"Rowley","full_name":"Rowley, Clarence W."}],"status":"public","intvolume":"        19","year":"2020"}