高次元ダイナミクスを制御する：スペクトル部分多様体への最適射影の学習
Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds
高次元非線形システムを低次元モデルに縮約する際、スペクトル部分多様体への最適な射影をデータから学習し、ロボット制御の精度を最大5倍改善した。
著者: Hugo Buurmeijer, Luis A. Pabon, John Irvin Alora, Roshan S. Kaundinya, George Haller, Marco Pavone
分類: eess.SY, cs.RO, cs.SY
原文アブストラクト
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art.
