Flexible ILC : towards a convex approach for non-causal rational basis functions

Iterative learning control (ILC) is subject to a trade-off between effective compensation of repeating disturbances, and amplification of non-repeating disturbances. Although important progress has been made in enhancing the flexibility of ILC to non-repeating tasks by means of basis functions, at present high performance comes at the cost of non-convex optimization. The aim of this paper is to develop a convex approach to ILC with rational basis functions. A key aspect of the proposed approach is the use of orthonormal basis functions in L2, such that non-causal control actions can be utilized. The benefits of using non-causal rational basis functions in ILC are demonstrated by means of a relevant example.