Signals associated with repetitive or rotating actions often have the form of periodic or multi-periodic nature and are also often subjected to forms of periodic disturbances. Much effort has been made to achieve perfect tracking results, while many of the previous results achieved small but not asymptotic zero tracking errors. The control schemes in this book, are therefore developed to achieve zero tracking error by either developing optimal control methodologies or a gradient based repetitive control method. Further implementation of the algorithms on a non-minimum phase spring-mass-damper system demonstrated the effectiveness of the algorithms. The algorithms in this book were initially designed for SISO (Single Input Single Output) tracking problems. However, under certain mathematical manipulations, these algorithms were also extended later for tracking problems of MIMO (Multi Input Multi Output) cases. Simulation tests also demonstrated their effectiveness.