学習ベース制御のための神経収縮計量の理論的概観：安定性保証付き
A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability
学習ベース制御の安定性を保証するため、最適収縮計量をニューラルネットでモデル化するNCMの理論を概説し、外乱下でも目標軌道との誤差が指数的に減少することを示した。
著者: Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques Slotine, Chuchu Fan
分類: cs.LG, cs.RO, cs.SY, eess.SY, math.OC
原文アブストラクト
This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient condition for incremental exponential stability of non-autonomous nonlinear system trajectories. Its innovation lies in providing formal robustness guarantees for learning-based control frameworks, utilizing contraction theory as an analytical tool to study the nonlinear stability of learned systems via convex optimization. In particular, we rigorously show in this paper that, by regarding modeling errors of the learning schemes as external disturbances, the NCM control is capable of obtaining an explicit bound on the distance between a time-varying target trajectory and perturbed solution trajectories, which exponentially decreases with time even under the presence of deterministic and stochastic perturbation. These useful features permit simultaneous synthesis of a contraction metric and associated control law by a neural network, thereby enabling real-time computable and probably robust learning-based control for general control-affine nonlinear systems.
