Turbocharger testing is a time consuming process, and as rapid-prototyping technology advances, so must other areas in the development chain. As an example, in one study a compressor map took over 34 hours to measure. In this paper, an effort to combat the main bottleneck of turbocharger testing, namely the thermal inertia, is made. When changing operating point during the measurement process, several minutes can be required before the turbocharger components reach temperature steady state. In an earlier paper, a method based on non-linear trajectory optimization was developed that significantly reduced the testing time required to produce compressor performance maps. The time was reduced by a factor of over 60, compared to waiting for the system to reach steady state with constant inputs. However, the method required a model of the turbocharger. This paper extends the method with system identification and model predictive control (MPC). This is an important step in order to use the optimal control method when only geometric information of the turbocharger is known, such as new prototypes. To demonstrate the effectiveness of the combination of system identification, non-linear trajectory optimization and MPC, the control strategy is applied to a virtual gas-stand implemented as a Simulink model, based on data from a Mitsubishi TD04 turbocharger. The data that was used to create the model was originally collected at Saab Automobile in Trollhättan, 2011. The results show that system identification captures the turbocharger behavior. Trajectory optimization finds a set of time optimal input trajectories. MPC successfully tracks the generated references. Real time implementation of the Matlab/Simulink based algorithm is planned for experimental testing.