Techniques are described herein for generating a dynamical systems control policy. A non-parametric family of smooth maps is defined on which vector-field learning problems can be formulated and solved using convex optimization. In some implementations, techniques described herein address the problem of generating contracting vector fields for certifying stability of the dynamical systems arising in robotics applications, e.g., designing stable movement primitives. These learning problems may utilize a set of demonstration trajectories, one or more desired equilibria (e.g., a target point), and once or more statistics including at least an average velocity and average duration of the set of demonstration trajectories. The learned contracting vector fields may induce a contraction tube around a targeted trajectory for an end effector of the robot. In some implementations, the disclosed framework may use curl-free vector-valued Reproducing Kernel Hilbert Spaces.