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Linear observer synthesis for nonlinear systems using Koopman Operator framework
Open accessAbstract
: In this paper we develop a new approach for observer synthesis for discrete time autonomous nonlinear systems based on Koopman operator theoretic framework. Koopman operator is a linear but an infinite-dimensional operator that governs the time evolution of system outputs in a linear fashion. We exploit this property to synthesize an observer form which enables the use of Luenberger/Kalman-like linear observers for nonlinear estimation. Using the techniques for Koopman eigenvalue/eigenfunction/mode computation, we describe a numerical procedure to construct such an observer form which is often valid in a large portion of state space or even globally. We numerically compare our approach with Extended Kalman Filter and report superior performance.
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Cites
Nonlinear controllability and observability
Hermann, R., & Krener, A. (1977) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1977.1101601 · Cited by 2,374 · cited 1×
“We will use standard notion of nonlinear observability Hermann and Krener (1977), which we briefly recall first.”
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Cited by
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Korda, M., & Mezić, I. (2018) · Automatica · doi:10.1016/j.automatica.2018.03.046 · Cited by 1,157
Chaos as an intermittently forced linear system
Brunton, S. L., Brunton, B. W., Proctor, J. L., Kaiser, E., & Kutz, J. N. (2017) · Nature Communications · doi:10.1038/s41467-017-00030-8 · Cited by 608
(2018) · IEEE Control Systems · doi:10.1109/mcs.2018.2810460 · Cited by 518
Metadata
- Authors
- Surana, A., & Banaszuk, A.
- Venue
- IFAC-PapersOnLine
- Publisher
- Elsevier BV
- Published
- 2016
- Volume
- 49
- Issue
- 18
- Pages
- 716-723
- ISSN
- 2405-8963 (ISSN-L)
- OpenAlex
- W2566199617
- Cited by
- 179
- References
- 1
- FWCI
- 15.99
- Type
- journal article
- Language
- en
- Open access
- diamond
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