In this paper, iterative learning control (ILC) of a class of non-affine-in-input processes is considered in Hilbert space, where the plant operators are quite general in the sense that they could be static or dynamic, differentiable or non-differentiable, continuous-time or discrete-time, and so forth. The control problem is first transformed to a problem of solving global implicit function to ensure the uniqueness of desired control input. Then, two contraction mapping-based ILC schemes are proposed in terms of the continuous differentiability of process model, where the learning convergence condition is derived through rigorous analysis. The proposed ILC schemes make full use of the process repetition, deal with system uncertainties easily, and are effective to infinite-dimensional or distributed parameter systems. In the end, the learning controller is applied to the boundary output control of a class of anaerobic digestion process for wastewater treatment. The control efficacy is verified by simulation. Copyright © 2013 John Wiley & Sons, Ltd.