---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Samuel E.
foaf_name: Otto, Samuel E.
foaf_surname: Otto
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: 0000-0002-3389-793X
- foaf_Person:
foaf_givenName: Clarence W.
foaf_name: Rowley, Clarence W.
foaf_surname: Rowley
dct_date: 2022^xs_gYear
dct_language: eng
dct_title: Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed
Trajectories@
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