Abstract : Among the several problems arising in the Airborne Wind Energy paradigm, an essential one is the control of the tethered airfoil trajectory during power generation. Tethered flight is a fast, strongly nonlinear, unstable and constrained process, motivating control approaches based on fast Non-linear Model Predictive Control. In this paper, a computationally efficient model is proposed, based on Differential-Algebraic equations. A control scheme based on Nonlinear Model Predictive Control (NMPC) and an estimator based on Moving Horizon Estimation (MHE) is proposed to handle the wind turbulences. In order to make a real-time application of Non-linear Model Predictive Control possible, a Real-Time Iteration scheme is proposed.