  Output reference tracking can be improved by iteratively learning from past
data to inform the design of feedforward control inputs for subsequent tracking
attempts. This process is called iterative learning control (ILC). This article
develops a method to apply ILC to systems with nonlinear discrete-time
dynamical models with unstable inverses (i.e. discrete-time nonlinear
non-minimum phase models). This class of systems includes piezoactuators,
electric power converters, and manipulators with flexible links, which may be
found in nanopositioning stages, rolling mills, and robotic arms, respectively.
As these devices may be required to execute fine transient reference tracking
tasks repetitively in contexts such as manufacturing, they may benefit from
ILC. Specifically, this article facilitates ILC of such systems by presenting a
new ILC synthesis framework that allows combination of the principles of
Newton's root finding algorithm with stable inversion, a technique for
generating stable trajectories from unstable models. The new framework, called
Invert-Linearize ILC (ILILC), is validated in simulation on a cart-and-pendulum
system with model error, process noise, and measurement noise. Where
preexisting Newton-based ILC diverges, ILILC with stable inversion converges,
and does so in less than one third the number of trials necessary for the
convergence of a gradient-descent-based ILC technique used as a benchmark.
