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Koopman NMPC: Koopman-based Learning and Nonlinear Model Predictive Control of Control-affine Systems [article]

Carl Folkestad, Joel W. Burdick
2021 arXiv   pre-print
Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems.  ...  The learned model is used for nonlinear model predictive control (NMPC) design where the bilinear structure can be exploited to improve computational efficiency.  ...  CONCLUSION This paper presented a method to combine the learning of lifted bilinear models based on Koopman spectral theory with nonlinear model predictive control.  ... 
arXiv:2105.08036v1 fatcat:iks63ayqabhzth4z6de5icf54u

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

Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems [article]

Giorgos Mamakoukas, Maria L. Castano, Xiaobo Tan, Todd D. Murphey
2021 arXiv   pre-print
When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX.  ...  This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives  ...  One can draw from many control schemes, including linear quadratic regulator (LQR) [3] , linear model predictive control (LMPC) [4] , nonlinear model predictive control (NMPC) [5] , feedback linearization  ... 
arXiv:2010.05778v2 fatcat:eqv2naaor5fcle7sowngy4kxl4

Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

Milan Korda, Igor Mezić
2018 Automatica  
We focus in particular on model predictive control (MPC) and show that MPC controllers designed in this way enjoy computational complexity of the underlying optimization problem comparable to that of MPC  ...  This paper presents a class of linear predictors for nonlinear controlled dynamical systems.  ...  By a predictor, we mean an artificial dynamical system that can predict the future state of a given nonlinear dynamical system based on the measurement of the current state and current and future inputs  ... 
doi:10.1016/j.automatica.2018.03.046 fatcat:rcvdnla225g5zpfc4nie4graam

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
., +, TAC Sept. 2020 3725-3727 Optimal Construction of Koopman Eigenfunctions for Prediction and Control.  ...  ., +, TAC June 2020 2550-2565 Lebesgue-Approximation Model Predictive Control of Nonlinear Sampled-Data Systems.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

Table of Contents

2022 IEEE Robotics and Automation Letters  
Murrieta-Cid Model Predictive Control and Transfer Learning of Hybrid Systems Using Lifting Linearization Applied to Cable Suspension Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ...  Reischl Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1109/lra.2022.3165102 fatcat:enjzebowe5hn7hsfwklc7nieuy

CFE-CMStatistics 2016 PROGRAMME AND ABSTRACTS 10th International Conference on CMStatistics 2016 Programme Committee

Angela Blanco-Fernandez, Gil Gonzalez-Rodriguez, Ana Colubi, Stella Hadjiantoni, M Dolores Jimenez-Gamero, Erricos Kontoghiorghes, George Loizou, Herman Van, Dijk, Peter Boswijk, Jianqing Fang, Alain Hecq (+123 others)
The aim is to show how various ideas coming from the nonlinear stability theory of functional differential systems, stochastic modeling, and machine learning, can be put together in order to create an  ...  We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets.  ...