A control system to control slip of a torque converter clutch includes a clutch plant model configured to predict a value of a parameter that relates to torque converter clutch slip as a function of clutch plant model inputs comprising commanded clutch pressure and of torque from the torque generative device. The control system also includes a model predictive controller configured to receive signals that allow determination of a desired value of the parameter that relates to torque converter clutch slip and a predicted value of the parameter that relates to torque converter clutch slip, receive a signal representing reported torque of the torque generative device, identify an optimal commanded clutch pressure value that will result in an optimal value of an objective function based on the clutch plant model, and provide a command signal to an actuator effective to control commanded clutch pressure to the torque converter clutch.