This paper deals with the problem of damping driveline oscillations, which is crucial to improving driveability and passenger comfort. This problem has received an increased interest due to the introduction of the dual-clutch powershift automatic transmission with dry clutches. This type of transmission improves fuel economy, but it results in a challenging control problem, due to driveline oscillations. These oscillations occur during gear-shift, while traversing backlash or when tip-in and tip-out maneuvers are performed. This paper presents the derivation of an accurate piecewise nonlinear drivetrain model with three inertias. Then, a horizon-1 predictive controller based on flexible Lyapunov functions is designed for the piecewise nonlinear drivetrain model. Several simulations show that the proposed control scheme can handle both the performance and physical constraints and the strict limitations on the computational complexity, while obtaining better performances compared to using PWA models of the vehicle drivetrain.