{"author":[{"first_name":"Samuel E.","last_name":"Otto","full_name":"Otto, Samuel E."},{"id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz"},{"full_name":"Rowley, Clarence W.","first_name":"Clarence W.","last_name":"Rowley"}],"title":"Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories","external_id":{"arxiv":["2209.09977"]},"citation":{"chicago":"Otto, Samuel E., Sebastian Peitz, and Clarence W. Rowley. “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories.” <i>ArXiv:2209.09977</i>, 2022.","ama":"Otto SE, Peitz S, Rowley CW. Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories. <i>arXiv:220909977</i>. Published online 2022.","bibtex":"@article{Otto_Peitz_Rowley_2022, title={Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories}, journal={arXiv:2209.09977}, author={Otto, Samuel E. and Peitz, Sebastian and Rowley, Clarence W.}, year={2022} }","apa":"Otto, S. E., Peitz, S., &#38; Rowley, C. W. (2022). Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories. In <i>arXiv:2209.09977</i>.","mla":"Otto, Samuel E., et al. “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories.” <i>ArXiv:2209.09977</i>, 2022.","ieee":"S. E. Otto, S. Peitz, and C. W. Rowley, “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories,” <i>arXiv:2209.09977</i>. 2022.","short":"S.E. Otto, S. Peitz, C.W. Rowley, ArXiv:2209.09977 (2022)."},"type":"preprint","publication":"arXiv:2209.09977","department":[{"_id":"655"}],"_id":"33461","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"date_updated":"2022-09-22T07:23:37Z","year":"2022","oa":"1","abstract":[{"text":"Data-driven models for nonlinear dynamical systems based on approximating the\r\nunderlying Koopman operator or generator have proven to be successful tools for\r\nforecasting, feature learning, state estimation, and control. It has become\r\nwell known that the Koopman generators for control-affine systems also have\r\naffine dependence on the input, leading to convenient finite-dimensional\r\nbilinear approximations of the dynamics. Yet there are still two main obstacles\r\nthat limit the scope of current approaches for approximating the Koopman\r\ngenerators of systems with actuation. First, the performance of existing\r\nmethods depends heavily on the choice of basis functions over which the Koopman\r\ngenerator is to be approximated; and there is currently no universal way to\r\nchoose them for systems that are not measure preserving. Secondly, if we do not\r\nobserve the full state, we may not gain access to a sufficiently rich\r\ncollection of such functions to describe the dynamics. This is because the\r\ncommonly used method of forming time-delayed observables fails when there is\r\nactuation. To remedy these issues, we write the dynamics of observables\r\ngoverned by the Koopman generator as a bilinear hidden Markov model, and\r\ndetermine the model parameters using the expectation-maximization (EM)\r\nalgorithm. The E-step involves a standard Kalman filter and smoother, while the\r\nM-step resembles control-affine dynamic mode decomposition for the generator.\r\nWe demonstrate the performance of this method on three examples, including\r\nrecovery of a finite-dimensional Koopman-invariant subspace for an actuated\r\nsystem with a slow manifold; estimation of Koopman eigenfunctions for the\r\nunforced Duffing equation; and model-predictive control of a fluidic pinball\r\nsystem based only on noisy observations of lift and drag.","lang":"eng"}],"status":"public","date_created":"2022-09-22T07:21:40Z","user_id":"47427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2209.09977.pdf"}],"language":[{"iso":"eng"}]}