MPC Design for CMG based testbed The growing interest in space exploration is focusing the research in the development of space architectures able to be independent and self-sustainable. To this end, different control strategies have been studied for different types of spacecrafts. The following thesis has the goal to design a Model Predictive Control approach for the attitude control of a spacecraft testbed equipped with 4 Control Moment Gyroscopes in pyramidal configuration. The CMGs are torque generators used for the attitude control of spacecrafts, and the principal problem in the implementation of these devices is that, in certain conditions, is impossible to provide torque along specific a direction.