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DTSTART;TZID=Europe/Brussels:20240415T130000
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DTSTAMP:20260502T171448
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UID:2117-1713186000-1713189600@www.naxys.be
SUMMARY:Benoît Bonnet-Weill (CNRS)
DESCRIPTION:Title : A Set-Valued Approach to Koopman Operators for Control Systems\n \nAbstract : In this talk\, I will present a new approach that we recently put forth together with Milan Korda (LAAS-CNRS) to define and study the properties of Koopman operators for general nonlinear control systems\, based on the theory of set-valued analysis. In this framework\, the Koopman operators at some given time are defined as the multi-mappings which\, to a given function observable\, associate the collection of its evaluations along all possible flows of the control systems. \nStarting from this general construct\, we were able to obtain relevant set-valued counterparts of all the basic results of Koopman theory\, namely the existence of an infinitesimal generator\, whose dynamics precisely encodes a rich subclass of observables\, an adapted version of the spectral mapping theorem relating their respective point spectra\, and a characterisation of the dual (also known as Perron-Frobenius) semigroup as a family of time-dependent operators acting on measures. \nBesides its conceptual soundness\, our approach provides theoretical grounding for a class of practical methods used for solving control problems by leveraging the Koopman framework\, which revolve around the idea of bundling together the classical Koopman operators stemming from a collection of fixed control inputs. \nThe seminar will take place in Room S08 at the Faculty of Sciences.
URL:https://www.naxys.be/event/benoit-bonnet-weill-cnrs/
CATEGORIES:NAXYS Seminar
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