Learning to Adapt: Reptile-D-Learning for Robust and Efficient Control Under Parametric Uncertainty

2026-06-24

AI Summary

This work addresses the challenge that conventional learning-based Lyapunov control struggles to guarantee stability and incurs costly retraining when system parameters are uncertain or vary. To overcome this, the paper introduces Reptile meta-learning into the D-learning framework for the first time, enabling the discovery of dynamical structures shared across systems with different parameters. This yields a generalizable initialization for Lyapunov neural networks and high-performance controllers without requiring an explicit dynamics model. The proposed approach significantly enhances rapid adaptation and generalization to unseen parameter configurations while rigorously ensuring closed-loop stability. Extensive experiments on multiple nonlinear control systems demonstrate its superior performance.

Abstract

Learning-based Lyapunov Control (LLC) provides formal stability guarantees for nonlinear systems, but its validity relies heavily on accurate system models. Parameter variations and uncertainties may invalidate stability constraints, leading to costly retraining. Although D-learning can estimate Lyapunov derivatives without relying on explicit dynamics models, it remains limited by single-task dynamics and degrades under large parameter shifts. We propose Reptile-D-learning, a framework that leverages the Reptile meta-learning algorithm to capture shared dynamical structures across systems with different parameters, thereby learning a generalizable Lyapunov network initialization and a high-performance controller. Experiments on multiple nonlinear control systems demonstrate that Reptile-D-learning significantly improves both generalization and rapid adaptation to unseen parameter configurations.

Problem

• parametric uncertainty
• Lyapunov control
• generalization
• nonlinear systems
• stability

Innovation

• Reptile-D-learning
• meta-learning
• Lyapunov control
• parametric uncertainty
• generalization