  When neural networks are used to model dynamics, properties such as stability
of the dynamics are generally not guaranteed. In contrast, there is a recent
method for learning the dynamics of autonomous systems that guarantees global
exponential stability using neural networks. In this paper, we propose a new
method for learning the dynamics of input-affine control systems. An important
feature is that a stabilizing controller and control Lyapunov function of the
learned model are obtained as well. Moreover, the proposed method can also be
applied to solving Hamilton-Jacobi inequalities. The usefulness of the proposed
method is examined through numerical examples.
