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Koopman Operator Spectrum for Random Dynamical Systems
Nelida Črnjarić-Žic, Senka Maćešić, Igor Mezić
In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum…
Data driven modal decompositions: analysis and enhancements
Zlatko Drmač, Igor Mezić, Ryan Mohr
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral anal…
Applied Koopman Operator Theory for Power Systems Technology
Yoshihiko Susuki, Igor Mezic, Fredrik Raak +1
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and…
Whole-Building Fault Detection: A Scalable Approach Using Spectral Methods
Michael Georgescu, Sophie Loire, Don Kasper +1
In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is an infinite-dimensional, linear ope…
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
Milan Korda, Igor Mezić
Extended Dynamic Mode Decomposition (EDMD) is an algorithm that approximates the action of the Koopman operator on an -dimensional subspace of the space of observables by sampli…
Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State Space Geometry
Igor Mezic
We examine spectral operator-theoretic properties of linear and nonlinear dynamical systems with globally stable attractors. Using the Kato Decomposition we develop a spectral expa…