  Hybrid systems have steadily grown in popularity over the last few decades
because they ease the task of modeling complicated nonlinear systems. Legged
locomotion, robotic manipulation, and additive manufacturing are representative
examples of systems benefiting from hybrid modeling. They are also prime
examples of repetitive processes; gait cycles in walking, product assembly
tasks in robotic manipulation, and material deposition in additive
manufacturing. Thus, they would also benefit substantially from Iterative
Learning Control (ILC), a class of feedforward controllers for repetitive
systems that achieve high performance in output reference tracking by learning
from the errors of past process cycles. However, the literature is bereft of
ILC syntheses from hybrid models. The main thrust of this dissertation is to
provide a boradly applicable theory of ILC for deterministic, discrete-time
hybrid systems, i.e. piecewise defined (PWD) systems. In summary, the three
main gaps addressed by this dissertation are (1) the lack of compatibility
between existing hybrid modeling frameworks and ILC synthesis techniques, (2)
the failure of ILC based on Newton's method (NILC) for systems with unstable
inverses, and (3) the lack of inversion and stable inversion theory for
piecewise affine (PWA) systems (a subset of PWD systems). These issues are
addressed by (1) developing a closed-form representation for PWD systems, (2)
developing a new ILC framework informed by NILC but with the new ability to
incorporate stabilizing model inversion techniques, and (3) deriving
conventional and stable model inversion theories for PWA systems.
