TY - GEN
T1 - Learning Koopman Operators with Control Using Bi-Level Optimization
AU - Huang, Daning
AU - Prasetyo, Muhammad Bayu
AU - Yu, Yin
AU - Geng, Junyi
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However, it still remains a challenging task to learn the Koopman operator with control from data, and in particular, the simultaneous identification of the Koopman linear dynamics and the mapping between the physical and Koopman states. Conventionally, the simultaneous learning of the dynamics and mapping is achieved via single-level optimization based on one-step or multi-step discrete-time predictions, but the learned model may lack model robustness, training efficiency, and/or long-term predictive accuracy. This paper presents a bi-level optimization framework that jointly learns the Koopman embedding mapping and Koopman dynamics with exact long-term dynamical constraints. Our formulation allows back-propagation in standard learning framework and the use of state-of-the-art optimizers, yielding more accurate and stable system prediction in long-time horizon over various applications compared to conventional methods.
AB - The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However, it still remains a challenging task to learn the Koopman operator with control from data, and in particular, the simultaneous identification of the Koopman linear dynamics and the mapping between the physical and Koopman states. Conventionally, the simultaneous learning of the dynamics and mapping is achieved via single-level optimization based on one-step or multi-step discrete-time predictions, but the learned model may lack model robustness, training efficiency, and/or long-term predictive accuracy. This paper presents a bi-level optimization framework that jointly learns the Koopman embedding mapping and Koopman dynamics with exact long-term dynamical constraints. Our formulation allows back-propagation in standard learning framework and the use of state-of-the-art optimizers, yielding more accurate and stable system prediction in long-time horizon over various applications compared to conventional methods.
UR - http://www.scopus.com/inward/record.url?scp=85173717741&partnerID=8YFLogxK
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U2 - 10.1109/CDC49753.2023.10383799
DO - 10.1109/CDC49753.2023.10383799
M3 - Conference contribution
AN - SCOPUS:85173717741
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2147
EP - 2152
BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 62nd IEEE Conference on Decision and Control, CDC 2023
Y2 - 13 December 2023 through 15 December 2023
ER -