Neural Lyapunov Control

TL;DR

This paper introduces a novel framework combining learning and falsification to design neural network Lyapunov functions for nonlinear control, providing stability guarantees and larger regions of attraction.

Contribution

It presents a new method that simplifies Lyapunov control design with provable stability, outperforming traditional approaches like LQR and SOS/SDP.

Findings

Achieves larger regions of attraction than existing methods.

Provides end-to-end correctness guarantees.

Demonstrates effectiveness on challenging control problems.

Abstract

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.