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The efficiency of power transmission through a Van Doorne type Continuously Variable Transmission (CVT) can be improved by allowing a small amount of relative slip between the engine and driveline side pulleys. However, excessive slip must be avoided to prevent transmission wear and damage. To enable fuel economy improvements without compromising drivability, a CVT control system must ensure accurate tracking of the gear ratio set-point while satisfying pointwise-in-time constraints on the slip, enforcing limits on the pulley forces, and counteracting driveline side and engine side disturbances. In this paper, the CVT control problem is approached from the perspective of Model Predictive Control (MPC). To develop an MPC controller, a low order nonlinear model of the CVT is established. This model is linearized at a selected operating point, and the resulting linear model is extended with extra states to ensure zero steady-state error when tracking constant set-points.