We consider the problem of controlling a vehicle moving towards an intersection by means of a remote controller over an unreliable channel. This channel affects both uplink communication (when the vehicle sends its state information to the controller) and downlink information (when the vehicle receives control actions from the controller). We propose a probabilistic framework to compute control actions at the controller in the presence of such unreliable communications. The controller is evaluated under different channel conditions and compared to two nominal controllers, one that assumes perfect communication and one that assumes no communication. We find that for low packet loss rates, the proposed controller leads to less aggressive control actions than the former and generally lower cost than the latter. We additionally consider the mismatch between the perceived knowledge of the channel at the controller, and the actual channel conditions. We evaluate the performance of our controller under this mismatch, which is of interest when the controller is designed.