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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.4
- 수록면
- 373 - 382 (10page)
- DOI
- 10.5302/J.ICROS.2024.24.0054
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초록· 키워드
오류제보하기
This paper briefly introduces the Koopman operator framework in the modeling and control of dynamic systems. The paper reviews the theoretical foundations of the Koopman operator, presenting implications for modeling and control in engineering systems. We describe the extended dynamic mode decomposition method to approximate the Koopman operator in a finite-dimensional space. We then show how an autoencoder is obtained for the approximated Koopman operator and analyze the uncertainty quantification. Numerical simulation reveals the validity of the proposed method. We also briefly review the interdisciplinary significance of the physics-informed Koopman operator and its potential to revolutionize the analysis and control of complex dynamic systems across various domains.
목차
Abstract
I. INTRODUCTION
II. KOOPMAN OPERATOR
III. KOOPMAN OPERATOR-BASED LINEAR MODELING
IV. QUANTIFICATION OF AUTOENCODER-BASED KOOPMAN OPERATOR
V. APPLICATIONS OF KOOPMAN OPERATOR AND PHYSICS-INFORMED TECHNIQUES
VI. CONCLUSIONS
REFERENCES
참고문헌 (23)
참고문헌 신청
B. O. Koopman, “Hamiltonian systems and transformation in Hilbert space,” Proceedings of the National Academy of Sciences of the United States of America, vol. 17, no. 5, p. 315, May. 1931. doi: https://doi.org/10.1073/pnas.17.5.315
M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica, vol. 93, pp. 149–160, Jul. 2018. doi: https://doi.org/10.1016/j.automatica.2018.03.046
Y. S. Quan, J. S. Kim, and C. C. Chung, “Linear parameter varying models-based gain-scheduling control for lane keeping system with parameter reduction,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 11, pp. 20 746–20 756, Nov. 2022. doi: https://doi.org/10.1109/TITS.2022.3188838
A. Mauroy, Y. Susuki, and I. Mezić, Koopman Operator in Systems and Control, Springer, Switzerland, 2020.
N. Takeishi, Y. Kawahara, and T. Yairi, “Learning Koopman invariant sub-spaces for dynamic mode decomposition,” Advances in Neural Information Processing Systems, CA, USA, vol. 30, pp. 1-11, 2017. doi:https://proceedings.neurips.cc/paper/2017/hash/3a835d3215755c435ef4fe9965a3f2a0-Abstract.html
M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica, vol. 93, pp. 149–160, Jul. 2018. doi: https://doi.org/10.1016/j.automatica.2018.03.046
Y. S. Quan, J. S. Kim, and C. C. Chung, “Linear parameter varying models-based gain-scheduling control for lane keeping system with parameter reduction,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 11, pp. 20 746–20 756, Nov. 2022. doi: https://doi.org/10.1109/TITS.2022.3188838
A. Mauroy, Y. Susuki, and I. Mezić, Koopman Operator in Systems and Control, Springer, Switzerland, 2020.
N. Takeishi, Y. Kawahara, and T. Yairi, “Learning Koopman invariant sub-spaces for dynamic mode decomposition,” Advances in Neural Information Processing Systems, CA, USA, vol. 30, pp. 1-11, 2017. doi:https://proceedings.neurips.cc/paper/2017/hash/3a835d3215755c435ef4fe9965a3f2a0-Abstract.html
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