Learning Koopman Operators with Control Using Bi-Level Optimization

Daning Huang, Muhammad Bayu Prasetyo, Yin Yu, Junyi Geng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2147-2152
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: Dec 13 2023Dec 15 2023

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period12/13/2312/15/23

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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