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Koopman Operator Inspired Nonlinear System Identification
SIAM Journal on Applied Dynamical Systems, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Decomposition theorems for koopman operators
Nonlinear Analysis: Theory, Methods & Applications, 1997Let \(L^1(X)= L^1_\mu(X)= L^1(X,\Sigma,\mu)\), \(L^\infty(X)= L^\infty_\mu(X)= L^\infty(X,\Sigma,\mu)\) denote the usual Lebesgue spaces on a \(\sigma\)-finite measure space \((X,\Sigma,\mu)\), and let \(S:X\to X\) be a non-singular map, i.e. \(\mu(A)=0\) implies \(\mu(S^{-1}(A))=0\), \(A\in\Sigma\). Denote \(\nu=\mu\circ S^{-1}\), \(\varphi= d\nu/d\mu\
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Koopman Operator Family Spectrum for Nonautonomous Systems
SIAM Journal on Applied Dynamical Systems, 2018For any non-autonomous dynamical system, the family of Koopman operators, as well as related Koopman eigenvalues and eigenfunctions, are parameterized by a time pair. Therefore, a logical approach in the data-driven algorithms for the non-autonomous Koopman mode decomposition is the application of a DMD method on the moving stencils of snapshots in ...
Maćešić, Senka +2 more
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KoopmanizingFlows: Diffeomorphically Learning Stable Koopman Operators
2021Submitted to the 4th Annual Learning for Dynamics & Control ...
Bevanda, Petar +5 more
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Sparsity Structures for Koopman and Perron--Frobenius Operators
SIAM Journal on Applied Dynamical Systems, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schlosser, Corbinian, Korda, Milan
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The extended Koopmans' theorem Fock operator
International Journal of Quantum Chemistry, 1987AbstractBy expanding the wave function of a system of N particles in terms of products of functions of one and (N‐1) particles, the one‐particle, nonlocal operator F̂EKT (extended Koopmans' theorem) is determined. It is shown that although this operator is nonhermitian, its eigenvalues and eigenfunctions represent the ionization energies and occupied ...
J. Mauricio O. Matos, Orville W. Day
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Koopman operator based nonlinear dynamic textures
2015 American Control Conference (ACC), 2015Dynamic texture (DT) is a simple yet powerful paradigm to model videos with repetitive spatiotemporal behavior. In this paper we propose a novel nonlinear approach for modeling complex DTs based on Koopman operator theoretic method. Koopman operator is linear but infinite dimensional operator, and captures full nonlinear behavior.
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LPV Modeling Using the Koopman Operator
2020Linear parameter-varying (LPV) models have been introduced to describe nonlinear (NL) and time-varying (TV) systems and make use of powerful results of linear control theory. LPV systems extend the notion of linear time invariant (LTI) systems, with the difference that the input/output relations change depending on a scheduling parameter.
Iacob, L.C. +2 more
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