Local Convergence Analysis of Damping for Zero-Order Optimization-Based Iterative Learning Control

Within the Iterative Learning Control (ILC) framework, damping is often introduced as a heuristic to facilitate convergence of the ILC iterates. We analyze how two simple damping approaches affect the local convergence behaviour of a zero-order optimization-based ILC method introduced in [1] and prove that the condition for local convergence, which is given in terms of the eigenvalues of an iteration matrix, can be relaxed if damping is introduced. Leveraging a simple example, we illustrate the effects of damping, which might be (1) convergence of an initially diverging iteration or (2) acceleration or deceleration of a converging iteration.