Neural Lyapunov Control of Unknown Nonlinear Systems with Stability GuaranteesDownload PDF

Published: 31 Oct 2022, Last Modified: 16 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: neural networks, nonlinear dynamics, Lyapunov function, nonlinear control, stability guarantees
TL;DR: We propose a learning framework to simultaneously learn and stabilize an unknown nonlinear system with provable guarantees.
Abstract: 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 with provable guarantees. 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 verifies the candidate Lyapunov function satisfies the Lyapunov conditions. We further provide theoretical guarantees of the proposed learning framework and show that the obtained Lyapunov function indeed verifies for the unknown nonlinear system under mild assumptions. We illustrate the effectiveness of the results with a few numerical experiments.
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