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SUMMARY: Data driven feedback control of nonlinear PDEs using the Koopman
operator - Dr Sebastian Peitz (University of Paderborn)
DTSTART;VALUE=DATE-TIME:20180514T140000
DTEND;VALUE=DATE-TIME:20180514T150000
UID:https://talks.ox.ac.uk/talks/id/e32a6d21-cadd-4db0-a37c-d0a2bd9888cf/
DESCRIPTION:In this talk we present a data driven reduced order modeling a
pproach for control of nonlinear PDEs which relies on the Koopman operator
. We construct a surrogate model for observations of the system state whic
h can be incorporated in an MPC framework. Two different approaches are co
nsidered. In the first one\, the dynamic control system is replaced by a f
inite set of autonomous systems with constant control inputs\, which trans
forms the control problem into a switching time problem. For each of these
systems\, the Koopman operator is approximated individually. Alternative
ly\, for systems depending linearly on the input\, we can construct a bili
near surrogate model by interpolating between two Koopman operators for co
nstant inputs. Using a recent convergence result for Extended Dynamic Mode
Decomposition\, convergence of the reduced order model based control prob
lem towards the true optimum can be shown. The resulting feedback controll
er is applied to several examples such as the 1D Burgers equation and the
2D Navier-Stokes equations. Furthermore\, experiments with an electrical d
rive demonstrate the practical use of the approach.\nSpeakers:\nDr Sebasti
an Peitz (University of Paderborn)
LOCATION:IEB building
URL:https://talks.ox.ac.uk/talks/id/e32a6d21-cadd-4db0-a37c-d0a2bd9888cf/
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DESCRIPTION:Talk: Data driven feedback control of nonlinear PDEs using the
Koopman operator - Dr Sebastian Peitz (University of Paderborn)
TRIGGER:-PT1H
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