We present a work-in-progress approach to improving driver attentiveness in cars provided with automated driving systems. The approach is based on a control loop that monitors the driver's biometrics (eye movement, heart rate, etc.) and the state of the car; analyses the driver's attentiveness level using a deep neural network; plans driver alerts and changes in the speed of the car using a formally verified controller; and executes this plan using actuators ranging from acoustic and visual to haptic devices. The paper presents (i) the self-adaptive system formed by this monitor-analyse-plan-execute (MAPE) control loop, the car and the monitored driver, and (ii) the use of probabilistic model checking to synthesise the controller for the planning step of the MAPE loop.