In this paper, we present an iterative learning algorithm for pulse-shape control applications of optical chirped pulse amplifiers for ultra-short, high-energy light pulses. For this, we first introduce a general nonlinear and infinite-dimensional mathematical model of chirped pulse amplifiers. By reducing the complexity of this detailed model and reformulating the control task, we are subsequently able to apply inversion-based iterative learning control to track desired output pulses. Using the reduced model to estimate both internal states and unknown parameters yields a fast and simple way of consistently estimating the input-output behavior without relying on a calibrated system model. The effectiveness of the resulting adaptive algorithm is finally illustrated with simulation scenarios on an experimentally validated mathematical model. (C) 2018 Elsevier Ltd. All rights reserved.