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Koopman Framework for Nonlinear Estimation

  • Amit SuranaEmail author
Chapter
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Part of the Lecture Notes in Control and Information Sciences book series (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.

Notes

Acknowledgements

The funding provided by UTRC is greatly appreciated.

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Copyright information

© United Technologies Research Center 2020

Authors and Affiliations

  1. 1.United Technologies Research CenterEast HartfordUSA

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