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This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system.
B. O. Koopman, “Hamiltonian systems and transformation in Hilbert space,” Proceedings of the National Academy of Sciences of the USA: Mathematics
1931
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J. M. Ortega, Matrix Theory
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A. Isidori, Nonlinear Control Systems
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J. Sarangapani, Neural Network Control of Nonlinear Discrete-Time Systems
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Y. Lan and I. Mezic, “Linearization in the large of nonlinear systems and Koopman operator spectrum,” Physica D
2013
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I. Mezic, “On applications of the spectral theory of the Koopman operator in dynamical systems and control theory,” Proceedings of IEEE 54th Conference on Decision and Control
2015
Cited alongside, same era.
2017
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M. Korda and I. Mezic, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica
2018
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B. Lusch, J. N. Kutz and S. L. Brunton, “Deep learning for universal linear embeddings of nonlinear dynamics,” Nature Communications
2018
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A. L. Bruce, V. M. Zeidan and D. S. Bernstein, “What is the Koopman operator? A simplified treatment for discrete-time systems,” Proceedings of 2019 American Control Conference
2020
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A. Mauroy, I. Mezic and Y. Susuki (Eds.), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications
2020
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J. Wang, Q. Dai, D. Shen, X. Song, X. Chen, S. Huang, and D. Filev, “Multi-agent navigation with collision avoidance: game theory approach,” Ford Report, October 2020
2020
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2021
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2019
Cited alongside, same era.
I. Abraham and T. D. Murphey, “Active learning of dynamics for data-driven control using Koopman operators,” IEEE Transactions on Robotics
2019
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
Cited in the paper.
2021
Later among the works it cites.
Q. H. Zhao and G. Tao, “Koopman system approximation based optimal control of multiple robots—Part II: Simulations and evaluations,” Manuscript 2023-05-02, May 2023 (submitted to arXiv)
2023
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