In this paper, we propose an optimal online tuning scheme for design-related scheduling parameters of adaptive Linear Parameter Varying (LPV) control systems. Specifically, the method is conceived within the Model Predictive Control (MPC) framework, which we demonstrate to ensure an inputto-state stable closed-loop and a recursively feasible optimisation program. The major advantage of the proposed solution is that it automatically determines the LPV scheduling parameters online, without the need to for the designer to develop any scheduling function (which is often a repetitive and obscure task). Moreover, it offers a direct and simple tuning procedure, able to directly incorporate multi-objective performance goals into a single quadratic cost. The proposed method is tested for an LPV Advanced Driver Assistance System, showing enhanced performances when compared to state-of-the-art methods based on nonlinear scheduling functions.