Fetching the paper…
Reading the bibliography…
Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator.
S. Boyd and L. Vandenberghe, Convex optimization . Cambridge university press, 2004
2004
Earlier work this paper cites.
B. D. Anderson and J. B. Moore, Optimal control: linear quadratic methods . Courier Corporation, 2007
2007
Earlier work this paper cites.
N. J. Higham, Functions of matrices: theory and computation . Siam, 2008, vol. 104
2008
Earlier work this paper cites.
J. B. Rawlings and D. Q. Mayne, Model predictive control: Theory and design . Nob Hill Pub. Madison, Wisconsin, 2009
2009
Earlier work this paper cites.
K. J. Aström and R. M. Murray, Feedback systems: an introduction for scientists and engineers . Princeton university press, 2010
2010
Earlier work this paper cites.
M. Budišić, R. Mohr, and I. Mezić, “Applied koopmanism,” Chaos: An Interdisciplinary Journal of Nonlinear Science , vol. 22, no. 4, p. 047510, 2012
2012
Earlier work this paper cites.
F. Allgöwer and A. Zheng, Nonlinear model predictive control . Birkhäuser, 2012, vol. 26
2012
Earlier work this paper cites.
E. Polak, Optimization: algorithms and consistent approximations . Springer Science & Business Media, 2012, vol. 124
2012
Earlier work this paper cites.
J. A. Paulson, A. Mesbah, S. Streif, R. Findeisen, and R. D. Braatz, “Fast stochastic model predictive control of high-dimensional systems,” in Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on . IEEE, 2014, pp. 2802–2809
2014
Earlier work this paper cites.
M. A. Patterson and A. V. Rao, “Gpops-ii: A matlab software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming,” ACM Transactions on Mathematical Software (TOMS) , vol. 41, no. 1, p. 1, 2014
2014
Cited alongside, same era.
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley, “A data–driven approximation of the koopman operator: Extending dynamic mode decomposition,” Journal of Nonlinear Science , vol. 25, no. 6, pp. 1307–1346, 2015
2015
Cited alongside, same era.
2016
Cited alongside, same era.
S. L. Brunton, B. W. Brunton, J. L. Proctor, and J. N. Kutz, “Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control,” PloS one , vol. 11, no. 2, 2016
2016
B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “Osqp: An operator splitting solver for quadratic programs,” in 2018 UKACC 12th International Conference on Control (CONTROL) . IEEE, 2018, pp. 339–339
2018
Later among the works it cites.
G. Mamakoukas, M. Castano, X. Tan, and T. Murphey, “Local koopman operators for data-driven control of robotic systems,” in Robotics: science and systems , 2019
2019
Later among the works it cites.
I. Abraham and T. D. Murphey, “Active learning of dynamics for data-driven control using koopman operators,” IEEE Transactions on Robotics , vol. 35, no. 5, pp. 1071–1083, 2019
2019
Later among the works it cites.
D. Bruder, B. Gillespie, C. D. Remy, and R. Vasudevan, “Modeling and control of soft robots using the koopman operator and model predictive control,” in Proceedings of Robotics: Science and Systems , FreiburgimBreisgau, Germany, June 2019
2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
2017
Cited alongside, same era.
2017
Cited alongside, same era.
A. Hereid and A. D. Ames, “Frost: Fast robot optimization and simulation toolkit,” in Intelligent Robots and Systems (IROS), 2017 IEEE/RSJ International Conference on . IEEE, 2017, pp. 719–726
2017
Cited alongside, same era.
P. Zhao, S. Mohan, and R. Vasudevan, “Control synthesis for nonlinear optimal control via convex relaxations,” in American Control Conference (ACC), 2017 . IEEE, 2017, pp. 2654–2661
2017
Cited alongside, same era.
M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica , vol. 93, pp. 149–160, 2018
2018
Cited alongside, same era.
2019
Later among the works it cites.
2020
Closest in time.
D. Goswami and D. A. Paley, “Global bilinearization and reachability analysis of control-affine nonlinear systems,” in The Koopman Operator in Systems and Control . Springer, 2020, pp. 81–98
2020
Closest in time.
S. Peitz, S. E. Otto, and C. W. Rowley, “Data-driven model predictive control using interpolated koopman generators,” SIAM Journal of Applied Dynamical Systems , vol. 19, no. 3, 2020
2020
Closest in time.