Neural Control Contraction Metric (CCM)

Please note that this is ongoing work. LQR baselines may be added for improved simulation results.

This repo explores neural Control Contraction Metrics (CCMs) for a nonlinear, underactuated cart–pendulum system.

• Control-affine dynamics: (ẋ = f(x) + B(x)u)
• Sin/cos state embedding to avoid angle discontinuities
• Learns a state-dependent contraction metric matrix (M(x)) and differential gain matrix (K(x))
• Enforces the continuous-time CCM condition on the closed-loop differential dynamics

This guarantees incremental (relative) exponential stability: nearby trajectories contract toward each other, as defined by a CCM-loop.

Structure

• python/train_ccm_metric.py --> CCM training
• matlab/cartpend_ccm_demo.m --> Nonlinear simulation + plots