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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 ...
Senka Macesic +2 more
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Koopman Operators for Estimation and Control of Dynamical Systems
Annual Review of Control, Robotics, and Autonomous Systems, 2021A common way to represent a system's dynamics is to specify how the state evolves in time. An alternative viewpoint is to specify how functions of the state evolve in time. This evolution of functions is governed by a linear operator called the Koopman operator, whose spectral properties reveal intrinsic features of a system.
Samuel E. Otto, Clarence W. Rowley
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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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Koopman Operator Dynamical Models: Learning, Analysis and Control
Annual Reviews in Control, 2021Stefan Sosnowski, Sandra Hirche
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Robust Tube-Based Model Predictive Control With Koopman Operators
Automatica, 2022Xinglong Zhang +2 more
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Koopman Operators for Modeling and Control of Soft Robotics
Current Robotics Reports, 2023Zhichao Liu +2 more
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Deep Learning Nonlinear Multiscale Dynamic Problems Using Koopman Operator
Journal of Computational Physics, 2021Lijian Jiang
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Policy Learning with Deep Koopman Operator Networks
2023 International Conference on Advanced Robotics and Mechatronics (ICARM), 2023Dongdong Zhao 0002 +3 more
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Koopman Operator-Based Model Identification and Control for Automated Driving Vehicle
International Journal of Control, Automation and Systems, 2023Chung Choo Chung +2 more
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