  The energy Casimir method is an effective controller design approach to
stabilize port-Hamiltonian systems at a desired equilibrium. However, its
application relies on the availability of suitable Casimir and Lyapunov
functions, whose computation are generally intractable. In this paper, we
propose a neural network-based framework to learn these functions. We show how
to achieve equilibrium assignment by adding suitable regularization terms in
the training cost. We also propose a parameterization of Casimir functions for
reducing the training complexity. Moreover, the distance between the
equilibrium of the learned Lyapunov function and the desired equilibrium is
analyzed, which indicates that for small suboptimality gaps, the distance
decreases linearly with respect to the training loss. Our methods are backed up
by simulations on a pendulum system.
