Linear identification of nonlinear systems: A lifting technique based on the Koopman operator [PDF]
, 2016 We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification ...
Goncalves, Jorge, Mauroy, Alexandre
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A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition [PDF]
, 2014 The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear ...
Kevrekidis, Ioannis G. +2 more
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Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework
Machine Learning: Science and Technology, 2023 Bernard O Koopman proposed an alternative view of dynamical systems based on linear operator theory, in which the time evolution of a dynamical system is analogous to the linear propagation of an infinite-dimensional vector of observables.
Said Ouala +4 more
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Data-Driven Koopman Model Predictive Control for Optimal Operation of High-Speed Trains
IEEE Access, 2021 Automatic train operation systems of high-speed trains are critical to guarantee operational safety, comfort, and parking accuracy. However, implementing optimal automatic operation control is challenging due to the train’s uncertain dynamics and ...
Bin Chen +7 more
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Data-driven Identification and Prediction of Power System Dynamics Using Linear Operators [PDF]
, 2019 In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust approach for data-
Ajjarapu, Venkataramana +4 more
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Robot Manipulator Control Using a Robust Data-Driven Method
Fractal and Fractional, 2023 Robotic manipulators with diverse structures find widespread use in both industrial and medical applications. Therefore, designing an appropriate controller is of utmost importance when utilizing such robots.
Mehran Rahmani, Sangram Redkar
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On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations [PDF]
, 2016 The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified.
McKeon, Beverley J. +2 more
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Mathematics, 2021 Inferring the latent structure of complex nonlinear dynamical systems in a data driven setting is a challenging mathematical problem with an ever increasing spectrum of applications in sciences and engineering.
Zlatko Drmač, Igor Mezić, Ryan Mohr
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Nonparametric Control Koopman Operators [PDF]
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental equivalences between different model representations, we are able to close the gap of control system operator ...
Bevanda, Petar +5 more
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Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator [PDF]
, 2016 In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g.
Goncalves, Jorge +2 more
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