二段階最適化による制御を伴うKoopman作用素の学習
Learning Koopman Operators with Control Using Bi-level Optimization
未知環境下の非線形ロボット系に対し、Koopman埋め込み写像と線形ダイナミクスを長期予測制約付きの二段階最適化で同時学習する手法を提案。
著者: Daning Huang, Muhammad Bayu Prasetyo, Yin Yu, Junyi Geng
分類: eess.SY, cs.RO, cs.SY
原文アブストラクト
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.
