  In this article, we present data-driven feedback linearization for nonlinear
systems with periodic orbits in the zero-dynamics. This scenario is challenging
for data-driven control design because the higher order terms of the internal
dynamics in the discretization appear as disturbance inputs to the controllable
subsystem of the normal form. Our design consists of two parts: a data-driven
feedback linearization based controller and a two-part estimator that can
reconstruct the unknown nonlinear terms in the normal form of a nonlinear
system. We investigate the effects of coupling between the subsystems in the
normal form of the closed-loop nonlinear system and conclude that the presence
of such coupling prevents asymptotic convergence of the controllable states. We
also show that the estimation error in the controllable states scales linearly
with the sampling time. Finally, we present a simulation based validation of
the proposed data-driven feedback linearization.
