Traffic control for large-scale urban road networks remains a challenging problem. Aggregated dynamical models of city-scale traffic, based on the macroscopic fundamental diagram (MFD), enable development of model-based perimeter control methods. Involving actuation over aggregated traffic flows, perimeter control specifies an effective and practicable congestion control solution. In this paper, we propose nonlinear model predictive perimeter control schemes, for regulation and economic optimization objectives, with closed-loop stability by construction. Macroscopic and microscopic simulations demonstrate the performance and domain of attraction properties of the proposed formulations. Results indicate potential of the methods for efficient and reliable control of city-scale traffic.