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This paper describes the design of a supervisory multivariable constrained Model Predictive Control (MPC) system for driver requested axle torque tracking with real-time fuel economy optimization that is scheduled for production by General Motors starting in 2018. The control system has been conceived and co-developed by General Motors and ODYS. The control approach consists of a set of linear MPC controllers scheduled in real-time based on powertrain operating conditions. For each MPC controller, a linear model is obtained by system identification with vehicle and dynamometer data. The supervisory MPC coordinates in real time desired Continuously Variable Transmission (CVT) ratio and desired engine torque to satisfy the system requirements, based on estimates of axle torque and engine fuel rate, by solving a constrained optimization problem at each sampling step. Each linear MPC controller is equipped with a Kalman filter to reconstruct the system state from available measurements.