Finite-data error bounds for Koopman-based prediction and control

DOI10.1007/s00332-022-09862-1OpenAlexW3194182445WikidataQ122930249 ScholiaQ122930249MaRDI QIDQ2105227

Friedrich Philipp, Karl Worthmann, Feliks Nüske, Sebastian Peitz, M. Schaller

Publication date: 8 December 2022

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.07102

zbMATH Keywords

nonlinear systemserror boundsKoopman operatordata-driven control

Mathematics Subject Classification ID

System identification (93B30) One-parameter semigroups and linear evolution equations (47D06) Operator-theoretic methods (93B28) Groups and semigroups of linear operators (47D03) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (4)

On the universal transformation of data-driven models to control systems ⋮ Koopman Operator Inspired Nonlinear System Identification ⋮ A unifying framework for tangential interpolation of structured bilinear control systems ⋮ Finite-data error bounds for Koopman-based prediction and control

Cites Work

• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• Variance reduction using nonreversible Langevin samplers
• On the numerical approximation of the Perron-Frobenius and Koopman operator
• Stability and feasibility of state constrained MPC without stabilizing terminal constraints
• Data-driven model reduction and transfer operator approximation
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• On convergence of extended dynamic mode decomposition to the Koopman operator
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Online estimation and adaptive control for a class of history dependent functional differential equations
• The Fokker-Planck equation. Methods of solutions and applications.
• Finite-data error bounds for Koopman-based prediction and control
• Data-driven approximation of the Koopman generator: model reduction, system identification, and control
• Extended dynamic mode decomposition for inhomogeneous problems
• Feedback control of nonlinear PDEs using data-efficient reduced order models based on the Koopman operator
• Koopman operator-based model reduction for switched-system control of PDEs
• Spectral properties of dynamical systems, model reduction and decompositions
• On the universal transformation of data-driven models to control systems
• Dynamic Mode Decomposition with Control
• A Vector-Valued Random Ergodic Theorem
• Spectral analysis of nonlinear flows
• Generalizing Koopman Theory to Allow for Inputs and Control
• Analysis and Geometry of Markov Diffusion Operators
• Data-Driven Model Predictive Control using Interpolated Koopman Generators
• Error Bounds for Dynamical Spectral Estimation
• Koopman analysis of quantum systems*
• Modern Koopman Theory for Dynamical Systems
• Prediction Accuracy of Dynamic Mode Decomposition
• Partial differential equations and stochastic methods in molecular dynamics
• Book Reviews

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