A global stabilizing control law is proposed for a non-minimum phase under-actuated planar vertical take-off and landing (PVTOL) aircraft. The proposed approach is based on receding horizon control and takes into account the positiveness of the thrust and its saturation to any arbitrary level. Moreover, the angular acceleration can also be bounded. Contrary to non-linear optimal control, the proposed approach, based on quadratic programming, improves significantly the computational cost of the algorithm and the convergence to a solution can be insured. The chosen cost function has a direct link with the energy needed to reach a desired point which is one of the main worries in the design of embedded control systems such as micro unmanned aerial vehicles (UAV).