Comparison of systems with complex behavior

By Igor Mezi'c, Andrzej Banaszuk. 2004

472 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/096af44d26fd3b797ea23e86d4bd06df7752d1bc

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In Computational Mechanics

In Statistics and Probability

Citations in the corpus

Multiresolution Dynamic Mode Decomposition (2015, methodology): “The origins of the DMD method, which arose from pioneering work connecting the Koopman operator to dynamical systems theory [10, 11], are associated with the ﬂuid dynamics community and the modeling of complex ﬂows [5, 6].”
Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses (2012, methodology): “Dynamic mode decomposition is a data-based method for estimating Koopman eigenvalues and modes. It approximates a trajectory, often from nonlinear dynamics, as the result of a linear process. The Ritz values of the decomposition yield growth rates and frequencies, and the Ritz vectors yield correspo”
Linearization in the large of nonlinear systems and Koopman operator spectrum (2013, methodology): “An effective way to approximate the linearization map systematically and in a more automatic manner would be computation of the associated Koopman eigenfunctions [7,4,35].”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, unknown): “Interest was revived once again in 2004 by Mezić and Banaszuk [33] and in 2005 by Mezić [31], who showed that Koopman theory could be used for the spectral analysis of nonlinear dynamical systems.”
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator (2017, methodology): “The research was initiated in [17, 15], using composition (Koopman) operator (1)Milan Korda and Igor Mezić are with the University of California, Santa Barbara, milan.”
Linear observer synthesis for nonlinear systems using Koopman Operator framework (2016, methodology): “A variety of techniques have been proposed in literature, including harmonic averaging (Mezic (2005); Mezic and Banaszuk (2004)), generalized Laplacian analysis (Budisic et al. (2012)), and Dynamic Mode Decomposition (DMD) and its variants, (see Tu et al. (2014) and references there in), and…”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “asurement functions [125,126]. This perspective did not gain traction until modern computation and data collection capabilities enabled the analysis of large volumes of measurement data. Mezic et al. [127,128,129,130,131,132] have developed much of the modern Koopman operator theory, and it has been”
Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics (2013, background): “(Note that these sets are called “isochrons” in [24], but we feel that the proper sense is “isostables” instead, in order to avoid the confusion with the isochrons of foci studied in [9, 28].)”
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control (2015, result): “Koopman analysis has been at the focus of recent data-driven efforts to characterize complex systems, since the work of Mezić and Banaszuk [11] and Mezić [12].”
Data-driven discovery of Koopman eigenfunctions for control (2017, background): “Since the seminal work of Mezić and Banaszuk [46] andMezić [42], Koopman theory has been the focus of efforts to characterize nonlinear systems.”
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control (2016, methodology): “The potential usefulness of such linear representations for prediction and control was suggested in [16].”