Human beings and many other species redirect their gaze towards targets of interest through rapid gaze shifts known as saccades, which are made approximately three to four times every second. While small saccades only rely on eye movements, larger ones result from coordinated movement of both eyes and head at the same time. Experimental studies have revealed that during saccades, the motor system manifests certain characteristics such as a stereotyped relationship between the relative contribution of eye and head to total gaze shift. Various optimality principles and several neural architectures have been suggested by researchers to explain these characteristics, but they do not involve incremental learning as a mechanism of optimization. Here, we suggest an open-loop neural controller with an adaptation mechanism which minimizes a proposed cost function. Simulations show that the characteristics of gaze shifts generated by this model match the experimental data in many aspects, in both head-restrained and head-free conditions. Therefore, our model can be regarded as a first step towards bringing together an optimality principle, a neural architecture, and an incremental learning mechanism into a unified control theory of saccadic gaze shifts.