High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

Dimitris Boskos, Jorge Cortes, Sonia Martinez

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Abstract

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control.

Original languageEnglish
Pages (from-to)797-812
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume69
Issue number2
DOIs
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Aerodynamics
  • Distributional uncertainty
  • estimation
  • linear system observers
  • Noise measurement
  • Optimization
  • Power system dynamics
  • Probability distribution
  • Random variables
  • stochastic systems
  • Uncertainty

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