  Stabilizing controller design and region of attraction (RoA) estimation are
essential in nonlinear control. Moreover, it is challenging to implement a
control Lyapunov function (CLF) in practice when only partial knowledge of the
system is available. We propose a learning framework that can synthesize
state-feedback controllers and a CLF for control-affine nonlinear systems with
unstructured uncertainties. Based on a regularity condition on these
uncertainties, we model them as bounded disturbances and prove that a CLF for
the nominal system (estimate of the true system) is an input-to-state stable
control Lyapunov function (ISS-CLF) for the true system when the CLF's gradient
is bounded. We integrate the robust Lyapunov analysis with the learning of both
the control law and CLF. We demonstrate the effectiveness of our learning
framework on several examples, such as an inverted pendulum system, a
strict-feedback system, and a cart-pole system.
