This paper presents a two step Iterative Learning Control (ILC) algorithm based on estimation and control with set-membership uncertainty (ECOset-ILC). The proposed method aims to design a feedforward input to iteratively improve a desired control task for nonlinear systems under the assumption of bounded-noise and/or binary/multi-valued sensors. The main contributions of this paper is the development of an ILC algorithm that combines a Set-Membership Estimation (SME), through ellipsoidal outer-bounding, and an Optimal Control Problem (OCP) that optimizes a control performance index and an Optimal Experiment Design (OED) objective to enforce a reduction of the uncertainty. The formulation of the proposed approach is detailed and its numerical implementation is discussed. Finally, to demonstrate the functioning of the approach a numerical example of the time-optimal motion planning of an overhead-crane with multi-valued measurement is presented.