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Koopman Framework for Nonlinear Estimation

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The Koopman Operator in Systems and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 484))

Abstract

In this chapter, we overview a new approach for nonlinear estimation based on Koopman operator-theoretic framework. We exploit Koopman eigenfunctions to create a nonlinear embedding/lifting of underlying nonlinear dynamics to synthesize observer forms (which we call Koopman observer form (KOF)) which enables the use of well-known estimation techniques developed for linear/bilinear systems in context of more general nonlinear systems. Furthermore, we present an extension of this framework for nonlinear constrained state estimation (CSE) with non-convex state constraints. Exploiting the KOF-based representation, we show that under certain conditions the CSE problem can be transformed into a higher dimensional but convex problem. We present a receding horizon estimation formulation based on this transformation, which could provide computational benefit in real-time applications. We also analyze system theoretic properties of KOF in relation to the original nonlinear system, and establish relationship between the original nonlinear estimation problem and the Koopman transformed problem. Finally, we illustrate our approach on a few examples.

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Acknowledgements

The funding provided by UTRC is greatly appreciated.

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Authors and Affiliations

  1. United Technologies Research Center, 411 Silver Lane, East Hartford, CT, 06118, USA

    Amit Surana

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  1. Amit Surana
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Correspondence to Amit Surana .

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Editors and Affiliations

  1. Department of Mathematics, University of Namur, Namur, Belgium

    Alexandre Mauroy

  2. Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA, USA

    Igor Mezić

  3. Department of Electrical and Information Systems, Osaka Prefecture University, Sakai, Japan

    Yoshihiko Susuki

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Surana, A. (2020). Koopman Framework for Nonlinear Estimation. In: Mauroy, A., Mezić, I., Susuki, Y. (eds) The Koopman Operator in Systems and Control. Lecture Notes in Control and Information Sciences, vol 484. Springer, Cham. https://doi.org/10.1007/978-3-030-35713-9_3

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