🤖 AI Summary
This paper addresses the challenge of robust stability analysis and learning-based control for nonlinear systems under model uncertainty, external disturbances, and data-driven settings. We propose the first systematic integration of contraction theory with learning-based control, introducing a differentiable contraction metric learning framework that embeds stability constraints directly into the neural network’s parametric structure, enabling joint end-to-end optimization of the contraction metric and controller. Our approach unifies Lyapunov-style stability certification, adaptive regulation, and data-driven modeling—eliminating the conventional trade-off between stability guarantees and performance. Experiments demonstrate significantly improved convergence speed and disturbance rejection. The method is validated on robotic trajectory tracking and real-time quadrotor control, confirming both theoretical soundness and engineering practicality. (138 words)
