Koopman-Based Lifting Techniques for Nonlinear Systems Identification
暂无分享,去创建一个
[1] Biao Huang,et al. System Identification , 2000, Control Theory for Physicists.
[2] I. Mezić,et al. Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.
[3] Clarence W. Rowley,et al. A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition , 2014, Journal of Nonlinear Science.
[4] I. Mezić. Spectral Properties of Dynamical Systems, Model Reduction and Decompositions , 2005 .
[5] R. Nagel,et al. One-parameter semigroups for linear evolution equations , 1999 .
[6] C. Kravaris,et al. Time-discretization of nonlinear control systems via Taylor methods , 1999 .
[7] C. David Remy,et al. Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theory , 2018, 2019 International Conference on Robotics and Automation (ICRA).
[8] M. Mackey,et al. Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics , 1998 .
[9] J. Collins,et al. Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.
[10] Steven L. Brunton,et al. Dynamic Mode Decomposition with Control , 2014, SIAM J. Appl. Dyn. Syst..
[11] I. Mezić,et al. Applied Koopmanism. , 2012, Chaos.
[12] Yoshihiko Susuki,et al. Nonlinear Koopman modes and power system stability assessment without models , 2014, 2014 IEEE PES General Meeting | Conference & Exposition.
[13] Bart De Moor,et al. Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .
[14] Giancarlo Ferrari-Trecate,et al. Fuzzy systems with overlapping Gaussian concepts: Approximation properties in Sobolev norms , 2002, Fuzzy Sets Syst..
[15] Guy-Bart Stan,et al. A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems , 2014, IEEE Transactions on Automatic Control.
[16] Günter Radons,et al. From dynamical systems with time-varying delay to circle maps and Koopman operators. , 2017, Physical review. E.
[17] Matthew O. Williams,et al. A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis , 2014, 1411.2260.
[18] Steven L. Brunton,et al. Sparse Identification of Nonlinear Dynamics with Control (SINDYc) , 2016, 1605.06682.
[19] Petre Stoica,et al. Decentralized Control , 2018, The Control Systems Handbook.
[20] Igor Mezic,et al. On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator , 2017, J. Nonlinear Sci..
[21] Lennart Ljung,et al. Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Exploring Matrix Logarithms , 2016, ArXiv.
[22] Richard D. Braatz,et al. On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.
[23] Xin Li,et al. On simultaneous approximations by radial basis function neural networks , 1998, Appl. Math. Comput..
[24] I. J. Leontaritis,et al. Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .
[25] Jake P. Taylor-King,et al. Operator Fitting for Parameter Estimation of Stochastic Differential Equations , 2017, 1709.05153.
[26] Jooyoung Park,et al. Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.
[27] Steven L. Brunton,et al. Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics , 2016, IEEE Transactions on Molecular, Biological and Multi-Scale Communications.
[28] J. Varah. A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations , 1982 .
[29] T. Brubaker,et al. Nonlinear Parameter Estimation , 1979 .
[30] VenancioAlvarez. GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS II , 2002 .
[31] Steven L. Brunton,et al. Data-driven discovery of Koopman eigenfunctions for control , 2017, Mach. Learn. Sci. Technol..
[32] Igor Mezic,et al. Global Stability Analysis Using the Eigenfunctions of the Koopman Operator , 2014, IEEE Transactions on Automatic Control.
[33] Junfeng Yang,et al. Alternating Direction Algorithms for 1-Problems in Compressive Sensing , 2009, SIAM J. Sci. Comput..
[34] J. Rogers. Chaos , 1876 .
[35] B. O. Koopman,et al. Hamiltonian Systems and Transformation in Hilbert Space. , 1931, Proceedings of the National Academy of Sciences of the United States of America.
[36] Lennart Ljung,et al. Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..
[37] Steven L. Brunton,et al. On dynamic mode decomposition: Theory and applications , 2013, 1312.0041.
[38] S. Brunton,et al. Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.
[39] N. Wiener,et al. Nonlinear Problems in Random Theory , 1964 .
[40] Igor Mezic,et al. Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control , 2016, Autom..
[41] Igor Mezic,et al. Linearization in the large of nonlinear systems and Koopman operator spectrum , 2013 .
[42] Aivar Sootla,et al. Geometric Properties of Isostables and Basins of Attraction of Monotone Systems , 2017, IEEE Transactions on Automatic Control.
[43] Igor Mezic,et al. Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator , 2016, SIAM J. Appl. Dyn. Syst..
[44] Heinz Unbehauen,et al. Structure identification of nonlinear dynamic systems - A survey on input/output approaches , 1990, Autom..
[45] Venancio Alvarez,et al. Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials II , 2002, Approximation Theory and its Applications.
[46] Alexandre Mauroy,et al. Linear identification of nonlinear systems: A lifting technique based on the Koopman operator , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).
[47] Marina Meila,et al. Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs , 2014, ArXiv.
[48] Benedetta Morini,et al. Computational Techniques for Real Logarithms of Matrices , 1996, SIAM J. Matrix Anal. Appl..
[49] Yonathan Bard,et al. Nonlinear parameter estimation , 1974 .
[50] Karl Johan Åström,et al. BOOK REVIEW SYSTEM IDENTIFICATION , 1994, Econometric Theory.
[51] A. Banaszuk,et al. Linear observer synthesis for nonlinear systems using Koopman Operator framework , 2016 .
[52] Guy-Bart Stan,et al. Online model selection for synthetic gene networks , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).
[53] R. Tibshirani. Regression Shrinkage and Selection via the Lasso , 1996 .
[54] P. Schmid,et al. Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.
[55] C. Caramanis. What is ergodic theory , 1963 .
[56] Ioannis G Kevrekidis,et al. Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator. , 2017, Chaos.
[57] Jean-Jacques E. Slotine,et al. Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis , 2016, IEEE Transactions on Signal Processing.