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This paper explores the application of Koopman operator theory to the control of robotic systems.
B. O. Koopman, “Hamiltonian systems and transformation in Hilbert space,” Proceedings of the National Academy of Sciences , vol. 17, no. 5, pp. 315–318, 1931
1931
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C. G. Atkeson, A. W. Moore, and S. Schaal, “Locally weighted learning for control,” in Lazy learning . Springer, 1997, pp. 75–113
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K. Zhou and J. C. Doyle, Essentials of robust control . Prentice hall Upper Saddle River, NJ, 1998, vol. 104
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G. Bradski, Dr. Dobb’s Journal of Software Tools , 2000
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J. Hauser, “A projection operator approach to the optimization of trajectory functionals,” IFAC Proceedings Volumes , vol. 35, no. 1, pp. 377–382, 2002
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M. Quigley, K. Conley, B. P. Gerkey, J. Faust, T. Foote, J. Leibs, R. Wheeler, and A. Y. Ng, “ROS: an open-source robot operating system,” in ICRA Workshop on Open Source Software , 2009
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N. Hovakimyan and C. Cao, L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation . SIAM, 2010
2010
Cited alongside, same era.
S. C. Ong, S. W. Png, D. Hsu, and W. S. Lee, “Planning under uncertainty for robotic tasks with mixed observability,” The International Journal of Robotics Research , vol. 29, no. 8, pp. 1053–1068, 2010
2010
Cited alongside, same era.
A. Bry and N. Roy, “Rapidly-exploring random belief trees for motion planning under uncertainty,” in International Conference on Robotics and Automation (ICRA) , 2011, pp. 723–730
2011
Cited alongside, same era.
D. Nguyen-Tuong and J. Peters, “Model learning for robot control: a survey,” Cognitive processing , vol. 12, no. 4, pp. 319–340, 2011
2011
Cited alongside, same era.
I. Mezić, “On applications of the spectral theory of the Koopman operator in dynamical systems and control theory,” in Decision and Control (CDC) , 2015, pp. 7034–7041
2015
Later among the works it cites.
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
Later among the works it cites.
D. Henrion, I. Mezic, and M. Putinar, “Applied Koopmanism,” 2016
2016
Later among the works it cites.
A. Mauroy and I. Mezić, “Global stability analysis using the eigenfunctions of the Koopman operator,” IEEE Transactions on Automatic Control , vol. 61, no. 11, pp. 3356–3369, 2016
2016
Later among the works it cites.
A. R. Ansari and T. D. Murphey, “Sequential action control: Closed-form optimal control for nonlinear and nonsmooth systems,” IEEE Transactions on Robotics , vol. 32, no. 5, pp. 1196–1214, Oct 2016
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2011
Cited alongside, same era.
K. J. Åström and B. Wittenmark, Adaptive control . Courier Corporation, 2013
2013
Cited alongside, same era.
I. Mezić, “Analysis of fluid flows via spectral properties of the Koopman operator,” Annual Review of Fluid Mechanics , vol. 45, pp. 357–378, 2013
2013
Cited alongside, same era.
M. Jordan and T. Mitchell, “Machine learning: Trends, perspectives, and prospects,” Science , vol. 349, no. 6245, pp. 255–260, 2015
2015
Cited alongside, same era.
2016
Later among the works it cites.
J. Van Den Berg, S. Patil, and R. Alterovitz, “Motion planning under uncertainty using differential dynamic programming in belief space,” in Robotics Research . Springer, 2017, pp. 473–490
2017
Closest in time.
G. Williams, N. Wagener, B. Goldfain, P. Drews, J. M. Rehg, B. Boots, and E. A. Theodorou, “Information theoretic mpc for model-based reinforcement learning,” International Conference on Robotics and Automation (ICRA) , 2017
2017
Closest in time.
A. Broad, T. D. Murphey, and B. Argall, “Learning models for shared control of human-machine systems with unknown dynamics,” Robotics: Science and Systems Proceedings , 2017
2017
Closest in time.