  We propose a new non-parametric framework for learning incrementally stable
dynamical systems x' = f(x) from a set of sampled trajectories. We construct a
rich family of smooth vector fields induced by certain classes of matrix-valued
kernels, whose equilibria are placed exactly at a desired set of locations and
whose local contraction and curvature properties at various points can be
explicitly controlled using convex optimization. With curl-free kernels, our
framework may also be viewed as a mechanism to learn potential fields and
gradient flows. We develop large-scale techniques using randomized kernel
approximations in this context. We demonstrate our approach, called contracting
vector fields (CVF), on imitation learning tasks involving complex
point-to-point human handwriting motions.
