Pollutant emissions and fuel economy objectives have led car manufacturers to develop innovative and more sophisticated engine layouts. In order to reduce time-to-market and development costs, recent research has investigated the idea of a quasi-systematic engine control development approach. Model based approaches might not be the only possibility but they are clearly predetermined to considerably reduce test bench tuning work requirements. In this paper, we present the synthesis of a physics-based nonlinear model predictive control law especially designed for powertrain control. A binary search tree is used to ensure real-time implementation of the explicit form of the control law, computed by solving the associated multi-parametric nonlinear problem.