S Zelenika, E Kamenar, M Korda, I. Mezić, "Application of Koopman-Based Control in Ultrahigh-Precision Positioning", https://link.springer.com/chapter/10.1007/978-3-030-35713-9_17
2020
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- A Mauroy, A Sootla, I. Mezić, "Koopman Framework for Global Stability Analysis", https://link.springer.com/content/pdf/10.1007/978-3-030-35713-9_2.pdf
- R Mohr, I. Mezić, "Koopman Spectrum and Stability of Cascaded Dynamical Systems", https://link.springer.com/content/pdf/10.1007/978-3-030-35713-9_5.pdf
- A Mauroy, Y Susuki, I. Mezić, "Introduction to the Koopman Operator in Dynamical Systems and Control Theory", https://link.springer.com/chapter/10.1007/978-3-030-35713-9_1
- Mauroy, Y Susuki, I. Mezić, "The Koopman Operator in Systems and Control: Theory, Numerics, and Applications", https://www.springer.com/gp/book/9783030357122
- Igor Mezić, "On Numerical Approximations of the Koopman Operator", arXiv:2009.05883
- Hiroya Nakao and Igor Mezić, "Spectral analysis of the Koopman operator for partial differential equations", Chaos
- M. Korda, I. Mezić, "Optimal construction of Koopman eigenfunctions for prediction and control", https://ieeexplore.ieee.org/document/9022864
- M Korda, I. Mezić, "Koopman Model Predictive Control of Nonlinear Dynamical Systems", https://www.nature.com/articles/s41467-020-15582-5
- Allan Avila & Igor Mezić, "Data-driven analysis and forecasting of highway traffic dynamics", https://www.nature.com/articles/s41467-020-15582-5
2019
- I Mezić, "Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry", https://epubs.siam.org/doi/abs/10.1137/18M1227688
- Zlatko Drmač, Igor Mezić, Ryan Mohr, "Data driven Koopman spectral analysis in Vandermonde-Cauchy form via the DFT: numerical method and theoretical insights", Data Driven Koopman Spectral Analysis in Vandermonde–Cauchy Form via the DFT: Numerical Method and Theoretical Insights
- Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran, Igor Mezić, "On the approximation of Koopman spectra for measure preserving transformations", https://epubs.siam.org/doi/10.1137/18M1175094
2018
- Hassan Arbabi, "Koopman spectral analysis and study of mixing in incompressible flows", UC Santa Barbara
- Ervin Kamenar, Milan Korda, Saša Zelenika, Igor Mezić, Senka Maćešić, "Koopman-based model predictive control of a nanometric positioning system", 18th EUSPEN International Conference
- Hassan Arbabi, Milan Korda, Igor Mezic, "A data-driven Koopman model predictive control framework for nonlinear flows", arXiv preprint arXiv:1804.05291
- Milan Korda, Igor Mezić, "Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control", Automatica
- Senka Maćešić, Nelida Črnjarić-Žic, Igor Mezić, "Non-autonomous Koopman operator family spectrum", Ninth Conference on Applied Mathematics and Scientific Computing
- A Mauroy, I Mezic, "Global computation of phase-amplitude reduction for limit-cycle dynamics", arXiv preprint arXiv:1803.07379
- Milan Korda, Yoshihiko Susuki, Igor Mezić, "Power grid transient stabilization using Koopman model predictive control", arXiv preprint arXiv:1803.10744
- Milan Korda, Igor Mezić, "On convergence of extended dynamic mode decomposition to the Koopman operator", Journal of Nonlinear Science
- Milan Korda, Mihai Putinar, Igor Mezić, "Data-driven spectral analysis of the Koopman operator", Applied and Computational Harmonic Analysis
- Milan Korda, Igor Mezić, "Learning Koopman eigenfunctions for prediction and control: the transient case", arXiv preprint arXiv:1810.08733
- N Črnjarić-Žic, S Maćešić, I Mezić, "Spectral properties of the stochastic Koopman operator and its numerical approximations", Ninth Conference on Applied Mathematics and Scientific Computing
- Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran, Igor Mezić, "On the approximation of Koopman spectra of measure-preserving flows", arXiv preprint arXiv:1806.10296
- Samaneh Sadri, Hassan Arbabi, Igor Mezic, Paolo Luzzatto Fegiz, "Koopman mode representations of vortex interactions and instabilities", Bulletin of the American Physical Society
- Senka Maćešić, Nelida Črnjarić-Žic, Igor Mezić, "Koopman Operator Family Spectrum for Nonautonomous Systems", Society for Industrial and Applied Mathematics
2017
- Hassan Arbabi, Igor Mezic, "Computation of Koopman spectrum for complex flows", SIAM meeting on applied dynamical systems, May 2017, Snowbird, Utah
- Nithin Govindarajan, Igor Mezic, "A toolbox for computing spectral properties of dynamical systems", SIAM meeting on applied dynamical systems, May 2017, Snowbird, Utah
- Hassan Arbabi and Igor Mezic, "Study of dynamics in post-transient flows using Koopman mode decomposition", Physical Review Fluids
- Igor Mezic and Hassan Arbabi, "On the Computation of Isostables, Isochrons and Other Spectral Objects of the Koopman Operator Using the Dynamic Mode Decomposition", 2017 International Symposium on Nonlinear Theory and Its Applications (NOLTA 2017) , Cancun, Mexico, December 4-7, 2017
- Milan Korda and Igor Mezic, "On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator", Journal of Nonlinear Science, 2017
- Milan Korda, Mihai Putinar and Igor Mezić, "Data-driven spectral analysis of the Koopman operator", https://arxiv.org/abs/1710.06532
2016
- Organizers: D. Henrion, I. Mezic, M. Putinar, "Oberwolfach Report. Mini-Workshop: Applied Koopmanism", Mathematisches Forschungsinstitut Oberwolfach. Feb. 7 - 13, 2016. Oberwolfach, Germany
- Hassan Arbabi and Igor Mezic, "Ergodic theory, Dynamic Mode Decomposition and computation of spectral properties of the Koopman operator", SIAM Journal on Applied Dynamical Systems, arXiv:1611.06664
- AS. Sharma, I. Mezic, BJ. McKeon, "On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations", To appear in Phys. Rev F
2015
- Hassan Arbabi, Igor Mezic, "Bifurcations of driven cavity flow and their implications for mixing", Bulletin of the American Physical Society, 60
- Michael Georgescu, Igor Mezić, "Building energy modeling: A systematic approach to zoning and model reduction using Koopman Mode Analysis", Energy and Buildings, Volume 86, January 2015, Pages 794–802
- Bryan Glaz, Sophie Loire, Maria Fonoberova, Igor Mezic, "Koopman decompositions of periodically forced Hopf bifurcation flows and application to dynamic stall", Bulletin of the American Physical Society, 60
- Zoran Levnajić, Igor Mezić, "Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi) periodic sets", Chaos 25, 053105 (2015); doi: 10.1063/1.4919767
- Alexandre Mauroy, I Mezić, "Extreme phase sensitivity in systems with fractal isochrons", Physica D 308 (2015) 40–51; doi: 10.1016/j.physd.2015.06.004
- Alexandre Mauroy, Igor Mezic, "Computation of the Koopman eigenfunctions is a systematic method for global stability analysis", SIAM Conference on Applications of Dynamical Systems (invited talk)
- Igor Mezic, "On applications of the spectral theory of the Koopman operator in dynamical systems and control theory", Decision and Control (CDC), 2015 IEEE 54th Annual Conference on
- Y. Susuhki, I. Mezic, H. Hoshino, T. Hikihara, "A Unified Definition of Collective Instabilities in Coupled Generator Networks", IFAC Papers Online
- Matthew O Williams, Clarence W Rowley, Igor Mezić, Ioannis G Kevrekidis, "Data fusion via intrinsic dynamic variables: An application of data-driven Koopman spectral analysis", EPL (Europhysics Letters), 109, (2015) 40007
2014
- Alexandre Mauroy, Igor Mezic, "Global stability analysis using the eigenfunctions of the Koopman operator", arXiv preprint arXiv:1408.137
- Michael Georgescu, "Analysis of systems in buildings using spectral Koopman operator methods", PhD Thesis, University of California Santa Barbara
- Igor Mezic, Hassan Arbabi, "On the relationship between Koopman Mode Decomposition and Dynamic Mode Decomposition", Bulletin of the American Physical Society, 59
- Ryan M. Mohr, "Spectral Properties of the Koopman Operator in the Analysis of Nonstationary Dynamical Systems", PhD Dissertation, University of California, Santa Barbara
- Yoshihiko Susuki, Igor Mezic, "Nonlinear Koopman modes and power system stability assessment without models", IEEE Transactions on Power Systems
- Alexandre Mauroy, Blane Rhoads, Jeff Moehlis, Igor Mezic, "Global isochrons and phase sensitivity of bursting neurons", SIAM Journal on Applied Dynamical Systems
2013
- A. Mauroy, I. Mezic, J. Moehlis, "Isostables, isochrons, and Koopman spectrum for the action–angle representation of stable fixed point dynamics", Physica D: Nonlinear Phenomena
- Y. Lan, I. Mezic, "Linearization in the large of nonlinear systems and Koopman operator spectrum", Physica D: Nonlinear Phenomena
- A. Mauroy, I. Mezic, "A spectral operator-theoretic framework for global stability", Decision and Control (CDC)
2012
- Marko Budišić, Igor Mezić, "Geometry of the ergodic quotient reveals coherent structures in flows", Physica D 241 (2012) 1255–1269
- Marko Budisic, "Ergodic Quotients in Analysis of Dynamical Systems", PhD Thesis, University of California Santa Barbara
- Marko Budišić, Ryan Mohr, Igor Mezić, "Applied Koopmanism", Chaos 22, 047510 (2012); doi: 10.1063/1.4772195
- Marko Budisic, Igor Mezic, "Visualization of invariant sets in incompressible fluid flows from Lagrangian data
", APS Meeting Abstracts - Alexandre Mauroy, Igor Mezić, "On the use of Fourier averages to compute the global isochrons of (quasi) periodic dynamics", Chaos 22, 033112 (2012)
2011
- Clarence W Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, Dan S Henningson, "Reduced-order models for flow control: balanced models and Koopman modes", Seventh IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Seventh IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009
2010
- Y. Susuki, I. Mezic, "Nonlinear Koopman modes of coupled swing dynamics and coherency identification", Power and Energy Society General Meeting
- Y. Susuki, I. Mezic, T. Hikihara, "Coherent swing instability of power systems and cascading failures", Power and Energy Society General Meeting
- CW. Rowley, I. Mezic, S. Bagheri, P. Schlatter, and DS. Henningson, "Reduced-order models for flow control: balanced models and Koopman modes", Seventh IUTAM Symposium on Laminar-Turbulent Transition
- Eisenhower, Bryan, Maile, T., Fischer, M. and Mezić, Igor, "Decomposing Building System Data for Model Validation and Analysis Using the Koopman Operator", IBPSA Simbuild Conference, NY, NY
- Mohr, Ryan and Mezi'c, Igor, "The use of ergodic theory in designing dynamics for search problems", Decision and Control (CDC), 2010 49th IEEE Conference on: 7300 -- 7307
2009
- Marko Budišic, Igor Mezic, "An Approximate Parametrization of the Ergodic Partition using Time Averaged Observables", Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, PR China: 3162--3168
- CW. Rowley, I. Mezic, S. Bagheri, P. Schlatter, DS. Henningson, "Spectral analysis of nonlinear flows", Journal of Fluid Mechanics
- Susuki, Yoshihiko and Mezić, Igor, "Ergodic partition of phase space in continuous dynamical systems", Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chienese Control Conference (CDC/CCC2009), Shanghai, China: 7497-7502
2008
- Levnajić, Zoran and Mezić, Igor, "Ergodic Theory and Visualization II: Visualization of Resonances and Periodic Sets", arXiv, nlin.CD
2007
- Hagen, Gregory, Smith, T, Banaszuk, Andrzej, Coifman, Ronald R and Mezić, Igor, "Validation of low-dimensional models using diffusion maps and harmonic averaging", Proceedings of the 46 th IEEE Conference on Decision and Control
2005
- Mezić, Igor, "Spectral properties of dynamical systems, model reduction and decompositions", Nonlinear Dynamics, 41: 309--325
2004
- Banaszuk, Andrzej, Mehta, P and Mezić, Igor, "Spectral balance: a frequency domain framework for analysis of nonlinear dynamical systems", Proceedings of the 43rd IEEE Conference on Decision and Control
- Mezić, Igor and Banaszuk, Andrzej, "Comparison of systems with complex behavior", Physica D: Nonlinear Phenomena, 197, 1-2: 101--133
1999
- Mezić, Igor and Wiggins, Stephen, "A method for visualization of invariant sets of dynamical systems based on the ergodic partition", Chaos, 9, 1
1994
- Igor Mezic, "On the geometrical and statistical properties of dynamical systems: theory and application", PhD Thesis, California Instituite of Technology