  We present a new method for learning control law that stabilizes an unknown
nonlinear dynamical system at an equilibrium point. We formulate a system
identification task in a self-supervised learning setting that jointly learns a
controller and corresponding stable closed-loop dynamics hypothesis. The
input-output behavior of the unknown dynamical system under random control
inputs is used as the supervising signal to train the neural network-based
system model and the controller. The proposed method relies on the Lyapunov
stability theory to generate a stable closed-loop dynamics hypothesis and
corresponding control law. We demonstrate our method on various nonlinear
control problems such as n-link pendulum balancing and trajectory tracking,
pendulum on cart balancing, and wheeled vehicle path following.
