Data-Driven Model Predictive Control using Interpolated Koopman Generators

DOI10.1137/20M1325678zbMath1461.49007arXiv2003.07094MaRDI QIDQ4983502

Clarence W. Rowley, Samuel E. Otto, Sebastian Peitz

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.07094

zbMATH Keywords

optimal controlmodel predictive controlreduced order modelingdynamic mode decompositionKoopman operator

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Dynamical systems in control (37N35) Linear composition operators (47B33) Existence theories for optimal control problems involving partial differential equations (49J20) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30) Numerical problems in dynamical systems (65P99)

Related Items

Extended dynamic mode decomposition for inhomogeneous problems, Koopman analysis of quantum systems*, Modern Koopman Theory for Dynamical Systems, Dissipativity-constrained learning of MPC with guaranteeing closed-loop stability, On the universal transformation of data-driven models to control systems, Data-driven inference of low order representations of observable dynamics for an airfoil model, Koopman Operator Inspired Nonlinear System Identification, Self-tuning model predictive control for wake flows, Robust tube-based model predictive control with Koopman operators, Estimation of the Koopman Generator by Newton's Extrapolation, Finite-data error bounds for Koopman-based prediction and control

Uses Software

• OpenFOAM

Cites Work

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• On the numerical approximation of the Perron-Frobenius and Koopman operator
• Machine learning control -- taming nonlinear dynamics and turbulence
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Direct methods with maximal lower bound for mixed-integer optimal control problems
• Resonances of a harmonically forced Duffing oscillator with time delay state feedback
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
• On convergence of extended dynamic mode decomposition to the Koopman operator
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
• Data-driven approximation of the Koopman generator: model reduction, system identification, and control
• 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
• Nonlinear model predictive control. Theory and algorithms
• Spectral properties of dynamical systems, model reduction and decompositions
• On dynamic mode decomposition: theory and applications
• Computational Methods for Fluid Dynamics
• Dynamic Mode Decomposition with Control
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Applied Koopmanism
• Discrete mechanics and optimal control: An analysis
• Dynamic mode decomposition of numerical and experimental data
• Tensor-based dynamic mode decomposition
• Spectral analysis of nonlinear flows
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Controlling chaos
• Generalizing Koopman Theory to Allow for Inputs and Control
• Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
• Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
• Low-order model for successive bifurcations of the fluidic pinball
• Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition
• MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION
• Linearly Recurrent Autoencoder Networks for Learning Dynamics