On Learning Discrete-Time Fractional-Order Dynamical Systems

Sarthak Chatterjee, S.D. Gonçalves Melo Pequito

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)
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Abstract

Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as electroencephalogram (EEG) and electrocorticogram (ECoG). Although learning the spatiotemporal parameters of DT-FODS is not a new problem, when dealing with neurophysiological signals we need to guarantee performance standards. Therefore, we need to understand the trade-offs between sample complexity and estimation accuracy of the system parameters. Simply speaking, we need to address the question of how many measurements we need to collect to identify the system parameters up to an uncertainty level. In this paper, we address the problem of identifying the spatial and temporal parameters of DT-FODS. The main result is the first result on non-asymptotic finite-sample complexity guarantees of identifying DT-FODS. Finally, we provide evidence of the efficacy of our method in the context of forecasting real-life intracranial EEG time series collected from patients undergoing epileptic seizures.
Original languageEnglish
Title of host publicationProceedings of the American Control Conference (ACC 2022)
PublisherIEEE
Pages4335-4340
ISBN (Print)978-1-6654-5196-3
DOIs
Publication statusPublished - 2022
Event2022 American Control Conference, ACC 2022 - Atlanta, United States
Duration: 8 Jun 202210 Jun 2022

Conference

Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States
CityAtlanta
Period8/06/2210/06/22

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

  • Uncertainty
  • Time series analysis
  • Measurement uncertainty
  • Estimation
  • Electroencephalography
  • Spatiotemporal phenomena
  • Complexity theory

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