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Towards a Data-Driven Bilinear Koopman Operator for Controlled Nonlinear Systems and Sensitivity Analysis

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Dynamic Data Driven Applications Systems (DDDAS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13984))

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Abstract

A Koopman operator is a linear operator that can describe the evolution of the dynamical states of any arbitrary uncontrolled dynamical system in a lifting space of infinite dimension. In practice, analysts consider a lifting space of finite dimension with a guarantee to gain accuracy on the state prediction as the order of the operator increases. For controlled systems, a bilinear description of the Koopman operator is necessary to account for the external input. Additionally, bilinear state-space model identification is of interest for two main reasons: some physical systems are inherently bilinear and bilinear models of high dimension can approximate a broad class of nonlinear systems. Nevertheless, no well-established technique for bilinear system identification is available yet, even less in the context of Koopman. This paper offers perspectives in identifying a bilinear Koopman operator from data only. Firstly, a bilinear Koopman operator is introduced using subspace identification methods for the accurate prediction of controlled nonlinear systems. Secondly, the method is employed for sensitivity analysis of nonlinear systems where it is desired to estimate the variation of a measured output given the deviation of a constitutive parameter of the system. The efficacy of the methods developed in this paper are demonstrated on two nonlinear systems of varying complexity.

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Acknowledgement

This material is based upon work supported by the AFOSR grant FA9550-15-1-0313 and FA9550-20-1-0176.

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Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, 16802, USA

    Damien Guého & Puneet Singla

Authors
  1. Damien Guého
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  2. Puneet Singla
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Correspondence to Damien Guého .

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Editors and Affiliations

  1. MOVEJ Analytics, Fairborn, OH, USA

    Erik Blasch

  2. InfoSymbiotic Systems Society, Bethesda, MD, USA

    Frederica Darema

  3. Air Force Research Laboratories, Canastota, NY, USA

    Alex Aved

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Guého, D., Singla, P. (2024). Towards a Data-Driven Bilinear Koopman Operator for Controlled Nonlinear Systems and Sensitivity Analysis. In: Blasch, E., Darema, F., Aved, A. (eds) Dynamic Data Driven Applications Systems. DDDAS 2022. Lecture Notes in Computer Science, vol 13984. Springer, Cham. https://doi.org/10.1007/978-3-031-52670-1_26

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  • DOI: https://doi.org/10.1007/978-3-031-52670-1_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52669-5

  • Online ISBN: 978-3-031-52670-1

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