未知の非線形システムに対する安定性保証付きニューラルリアプノフ制御
Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees
未知の非線形システムに対し、ニューラルネットワークで制御器とリアプノフ関数を同時に学習し、SMTソルバで安定性を検証する枠組みを提案。
著者: Ruikun Zhou, Thanin Quartz, Hans De Sterck, Jun Liu
分類: eess.SY, cs.LG, cs.RO, cs.SY, math.DS
原文アブストラクト
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller. The SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. We provide theoretical guarantees of the proposed learning framework in terms of the closed-loop stability for the unknown nonlinear system. We illustrate the effectiveness of the approach with a set of numerical experiments.
