Modeling of hydraulic clutch transmissions is far from straightforward due to their nonlinear hybrid dynamics, i.e. switching between three dynamic phases. In this paper we identify a local linear model only for the constrained first phase, based on which a predictive controller is used to track a suitable engagement signal. The robustness of this controller in the latter two phases is guaranteed by making the constraints inactive and pre-tuning the control parameters based on its closed loop formulation and applying robust stability theorem. This controller is then implemented in real-time on a wet-clutch test setup and is shown to achieve optimal engagement.