Iterative Learning Control is a control strategy to improve performance over repeated attempts at a certain task. By recording the signals generated from the previous attempt, a feedforward control signal can be generated to improve performance in the next attempt. The use of information from the previous iteration means that ILC is a feedback controller in the iteration domain. As with any feedback controller, there is the possibility of divergence, or instability, resulting in unbounded control signals. For nonlinear systems, convergence criteria for ILC systems are known for several specific cases, including the popular noncausal adjoint- and Newton-step update laws. In this thesis we develop a more general framework for certifying the convergence of nonlinear, noncausal ILC systems which includes, but is not limited to, the aforementioned specific cases. We do so using contraction theory, resulting in a convex convergence certificate, which is amenable to numerical computation.
The other major topic in this thesis is the application of ILC to dynamic walking robots. Dynamic walking robots have the potential for versatile, efficient, and lifelike locomotion, but are often difficult to control, due to underactuation and undermodelling. ILC is known to be robust to undermodelling; however, ILC cannot be applied directly to dynamic walking robots, due to underactuation. We propose a variant of ILC suitable for dynamic walking robots that uses a phase variable as an index variable instead of using time. ``Phase-indexing'' ILC allows better control of dynamic walking robots, including learning to perform more prescribed motions more accurately, and in a more energy efficient way. Hardware experiments on a 2 degree of freedom compass-gait walking robot and simulation results on the compass-gait and 5-link dynamic walking robot verify the efficacy of the proposed method.