Robust Neural Lyapunov Control for Nonlinear Systems With Quadratically Bounded Disturbances

ABSTRACT In this work, we propose a learning framework that can synthesize a robust control Lyapunov function and a stable state‐feedback controller for general nonlinear systems with quadratically bounded disturbances. While theoretically appealing, traditional approaches based on control Lyapunov functions face significant practical challenges due to unmodeled disturbances and estimation errors. To address this issue, our work employs a learning‐based approach that combines Lyapunov analysis with machine‐learning techniques. Additionally, we propose a random sampling‐based method to verify the validity of the Lyapunov condition. Furthermore, we extend our approach to synthesize stable controllers for control‐affine systems with unstructured uncertainties and actively learn the uncertainty from system trajectories. Finally, we show the effectiveness of our approach on four examples: the inverted pendulum, a third‐order strict‐feedback system, the cart‐pole system, and the 2D quadrotor system.