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SUMMARY:Capture\, Propagate\, and Control Distributional Uncertainty
DTSTART:20230630T110000
DTEND:20230630T120000
DTSTAMP:20260414T181542Z
UID:914a83bc9953a9edc822ff1a2437110f44cd3d378fe87e4efd964d06
CATEGORIES:Conferences - Seminars
DESCRIPTION:Liviu Aolaritei (ETH Zürich)\nAbstract: \nUncertainty propag
 ation has established itself as a fundamental area of research in all fiel
 ds of science and engineering. Among its central topics stands the problem
  of modeling and propagating distributional uncertainty\, i.e.\, uncertain
 ty about probability distributions. In this talk\, we employ tools from Op
 timal Transport (OT) to capture distributional uncertainty via OT ambiguit
 y sets\, which we show to be very natural and expressive\, and to enjoy po
 werful geometrical\, computational\, and statistical features and guarante
 es. We show that these ambiguity sets propagate nicely and intuitively thr
 ough linear and nonlinear (possibly corrupted by stochastic noise) transf
 ormations\, and that in many cases the result of the propagation is again 
 an OT ambiguity set. Moreover\, whenever this is not the case\, we show th
 at the result of the propagation can be tightly upper bounded by another O
 T ambiguity set. \n\nWe then specialize our results to stochastic LTI sys
 tems where only partial statistical information about the noise is availa
 ble (e.g.\, samples)\, and start by showing that distributional uncertaint
 y can be efficiently captured\, with high probability\, within an OT ambig
 uity set on the space of noise trajectories. Then\, we show that such ambi
 guity sets propagate exactly through the system dynamics\, giving rise to 
 stochastic tubes that contain\, with high probability\, all trajectories o
 f the stochastic system. Finally\, we show that the control task is very i
 nterpretable\, unveiling an interesting decomposition between the roles of
  the feedforward and the feedback control terms. This theory is successful
 ly exploited to formulate a Wasserstein Tube MPC capable of optimally trad
 ing between safety and performance.\n\nBio: \nLiviu Aolaritei is a PhD s
 tudent in the Automatic Control Lab at ETH Zürich. Prior to his PhD\, he
  received a Master Degree in Robotics\, Systems\, and Control from ETH 
 Zürich\, and a Bachelor Degree in Information Engineering from the Univ
 ersity of Padova. During his PhD he was a visiting graduate student in the
  Operations Research Center at MIT\, and in the IEOR Department at Columbi
 a University. His current research interests revolve around Distributional
 ly Robust Optimization and Optimal Transport\, as well as their applicati
 on in Automatic Control\, Machine Learning\, Operations Research\, and Ene
 rgy Systems.
LOCATION:ME C2 405 https://plan.epfl.ch/?room==ME%20C2%20405
STATUS:CONFIRMED
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