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Optimal control formulation of pulse-based control using Koopman operator

Aivar Sootla, Alexandre Mauroy, Damien Ernst
2018 Automatica  
One of the main advantages of using the Koopman operator is the powerful computational tools developed for this framework.  ...  We show that this problem can be solved using a static optimization problem in the case of monotone systems.  ...  Our formulation based on the isostables is guided by our use of the Koopman operator framework for computational purposes. However, there are other benefits in this formulation.  ... 
doi:10.1016/j.automatica.2018.01.036 fatcat:36avoe4ixfcyzlsrteypdcvmka

Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty

Aivar Sootla, Damien Ernst
2018 IEEE Transactions on Automatic Control  
Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems.  ...  In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses).  ...  Without loss of generality, we assume that for monotone systems s 1 (x) is such that ∇s 1 (x) 0 for all x ∈ B(x * ). III. PULSE-BASED CONTROL USING KOOPMAN OPERATOR A.  ... 
doi:10.1109/tac.2017.2736941 fatcat:vmeamib4rnbo5ddgsj7ionn6v4

Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty [article]

Aivar Sootla, Damien Ernst
2017 arXiv   pre-print
Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems.  ...  In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses).  ...  Without loss of generality, we assume that for monotone systems s 1 (x) is such that ∇s 1 (x) 0 for all x ∈ B(x * ). III. PULSE-BASED CONTROL USING KOOPMAN OPERATOR A.  ... 
arXiv:1708.00232v1 fatcat:rt4nxltibbdzjg4tudbbppdgim

Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries [article]

Carl Folkestad, Skylar X. Wei, Joel W. Burdick
2021 arXiv   pre-print
Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable to optimal control.  ...  Nonlinear dynamical effects are crucial to the operation of many agile robotic systems.  ...  CONCLUSION The coupling of Koopman-based bilinear models and NMPC allows for real-time optimal control of robots that captures important nonlinearities, while allowing for critical state and control limits  ... 
arXiv:2110.10341v1 fatcat:jmxzcghyorer7fuyvy3z77wqyy

Handling plant-model mismatch in Koopman Lyapunov-based model predictive control via offset-free control framework [article]

Sang Hwan Son, Abhinav Narasingam, Joseph Sang-Il Kwon
2020 arXiv   pre-print
based on a disturbance estimator approach and ensures feasibility and stability of the control system by applying Lyapunov constraints to the optimal control problem.  ...  In this work, we present offset-free Koopman Lyapunov-based model predictive control (KLMPC) framework that addresses the inherent plant-model mismatch in KMPC schemes using an offset-free control framework  ...  Acknowledgments Financial support from the Artie McFerrin department of chemical engineering and the Texas A&M Energy Institute are gratefully acknowledged.  ... 
arXiv:2010.07239v1 fatcat:cbohssflajb57ogvkoau3qeucq

Bilinear dynamic mode decomposition for quantum control [article]

Andy Goldschmidt, Eurika Kaiser, Jonathan L. Dubois, Steven L. Brunton, J. Nathan Kutz
2020 arXiv   pre-print
Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many  ...  The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure.  ...  Indeed, an operator-theoretic linearization of classical dynamical systems was contemporaneously made using the Koopman-von Neumann theory [29, 30] .  ... 
arXiv:2010.14577v2 fatcat:tiu4ylmzxnhodco3hny5k5typm

Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach [article]

Dan Wilson
2021 arXiv   pre-print
proposed optimal control formulations.  ...  The adaptive phase-amplitude reduced equations allow for a numerically tractable optimal control formulation and the associated optimal stimuli significantly outperform those resulting from from previously  ...  Two Alternative Optimal Control Formulations In addition to the optimal control formulation that uses the adaptive phase-amplitude reduction, two additional control formulations used for comparison purposes  ... 
arXiv:2102.04535v1 fatcat:jr64t6wg35b3njmylptq7l2vma

Model predictive control for robust quantum state preparation [article]

Andy J. Goldschmidt, Jonathan L. DuBois, Steven L. Brunton, J. Nathan Kutz
2022 arXiv   pre-print
We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation.  ...  MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to  ...  (b) Under the hood of the A operation, robust control pulses are designed using model predictive control (MPC).  ... 
arXiv:2201.05266v1 fatcat:l75qldtbizeixewocjyozreyhi

Self-Organization in Networks: A Data-Driven Koopman Approach [article]

Claudia Caro-Ruiz, Duvan Tellez-Castro, Andres Pavas, Eduardo Mojica-Nava
2017 arXiv   pre-print
Networks out of equilibrium display dynamics characterized by multiple equilibria and sudden transitions.  ...  To illustrate these ideas, we use synchronized behavior from an Integral-and-Fire oscillators (IFO) system and SOC in the Bak-Sneppen model.  ...  Also, we will use Koopman operator approach for the design of control systems to reduce size and frequency of avalanches in SOC phenomena.  ... 
arXiv:1709.09576v1 fatcat:uw2y5vtq4ferrkki6g6axbcmpu

Chaos as an intermittently forced linear system

Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, Eurika Kaiser, J. Nathan Kutz
2017 Nature Communications  
This work combines Takens' delay embedding with modern Koopman operator theory and sparse regression to obtain linear representations of strongly nonlinear dynamics.  ...  The result is a decomposition of chaotic dynamics into a linear model in the leading delay coordinates with forcing by low energy delay coordinates; we call this the Hankel alternative view of Koopman  ...  ., a matrix K) of the Koopman operator is therefore an important goal of data-driven analysis and control; this relies on a measurement subspace that remains invariant to the Koopman operator [15] .  ... 
doi:10.1038/s41467-017-00030-8 pmid:28559566 pmcid:PMC5449398 fatcat:ihh4dvl3cjahxil53qbqfjbgme

Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear Operators

Shervin Bagheri
2012 Archives of Computational Methods in Engineering  
This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory.  ...  Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provide a means to gain physical insight into the dynamics  ...  The starting point of modern optimal and robust control design is an input-output formulation.  ... 
doi:10.1007/s11831-012-9074-0 fatcat:wesb356mgverdag2i6nx7yvyte

Model-Free Information Extraction in Enriched Nonlinear Phase-Space [article]

Bin Li, Yueheng Lan, Weisi Guo, Chenglin Zhao
2018 arXiv   pre-print
determined by the Koopman operator.  ...  This dramatically improves over commonly used static local features, which are vulnerable to unknown transitions or noise.  ...  KT (x n ) = T (x n+1 ), the Koopman operator provides a way to identify the linearization transformation of complex nonlinear dynamics, implemented numerically via Koopman mode decomposition (KMD) or dynamic  ... 
arXiv:1804.05170v2 fatcat:hqnutpwdgfh45ide5td7pru424

System identification of a hysteresis-controlled pump system using SINDy [article]

Gregor Thiele, Arne Fey, David Sommer, Jörg Krüger
2020 arXiv   pre-print
Hysteresis-controlled devices are widely used in industrial applications.  ...  Dynamic models of systems are essential for optimizing such industrial supply technology. However, conventional system identification approaches can hardly handle hysteresis-controlled devices.  ...  His hysteron-operator allows for approximation of natural hysteresis using weighted stairs.  ... 
arXiv:2003.07465v5 fatcat:2n5ia5sejbh3rg3wtugxuv7zda

A data-driven Koopman model predictive control framework for nonlinear flows [article]

Hassan Arbabi, Milan Korda, Igor Mezic
2018 arXiv   pre-print
In the first step, we compute a Koopman-linear representation of the control system using a variation of the extended dynamic mode decomposition algorithm and then we apply model predictive control to  ...  The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.  ...  Sebastian Peitz for a constructive exchange of ideas on the subject. This research was supported in part by the ARO-MURI grant W911NF-17-1-0306, with program managers Dr. Matthew Munson and Dr.  ... 
arXiv:1804.05291v2 fatcat:e6c477z3ongvret5z5wpe4km6a

POD-spectral decomposition for fluid flow analysis and model reduction

A. Cammilleri, F. Gueniat, J. Carlier, L. Pastur, E. Memin, F. Lusseyran, G. Artana
2013 Theoretical and Computational Fluid Dynamics  
The approach is illustrated using time resolved PIV data of a cylinder wake flow with associated Reynolds number equal to 3900.  ...  We propose an algorithm that combines Proper Orthogonal Decomposition with a spectral method to analyse and extract from time data series of velocity fields, reduced order models of flows.  ...  Spectral mode decomposition based on Koopman operator This second family of techniques relies on a spectral decomposition inspired on the Koopman operator theory.  ... 
doi:10.1007/s00162-013-0293-2 fatcat:lpwcba7tjrccjasurolhg2q56e
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