System identification methods build mathematical models of dynamical systems based on observed data. The intended use of the model should always be reflected in the methods and techniques used for identification. In this paper an identification scheme is derived for the case where the model is going to be used for GMC controller design. The aim of GMC control is to make the output approach a setpoint along a given desired trajectory. This is reflected in the identification scheme which is non-standard in two ways. Firstly, the emphasis is on the output trajectories of the models, and secondly we try to make the prediction errors follow an error trajectory determined by the controller parameters. Simulation studies are included which show that the derived identification scheme performs well.