Neural Stochastic Contraction Metrics at UTIAS
Learning-based stability analysis for nonlinear stochastic systems
TLDR
I built a PyTorch pipeline to learn stochastic contraction metrics and applied it to a control contraction metric loop for a toy system. A neural network parameterizes a Riemannian metric M(x) that satisfies a contraction inequality, giving stability guarantees even with stochastic noise. Next up: pushing this to 360° roll trajectories for racing drones.
Project background
Last summer, I spent some time up at the University of Toronto Institute for Aerospace Studies (UTIAS) in the Flight Systems & Control Lab. From my prior experience with control systems through robotics and rocketry, I assisted Master's student (and recently graduated!) Kevin Chen in his thesis regarding quadrotor with slung payload CCM Loops. The question was whether a neural network could learn a stochastic contraction metric—a Riemannian metric M(x) that certifies exponential stability even when the system is driven by noise.
Instead of hand-designing Lyapunov functions or metrics, the idea is to parameterize M(x) with a neural network and train it so that a matrix inequality from contraction theory is satisfied across the state space. If you can make that inequality hold everywhere, you get a global stability guarantee “for free”.
Write-up still in progress.. come back later for more details!