A propulsion system, control system, and method use model predictive control systems to generate a plurality of sets of possible command values and determine a cost for each set of possible command values. The set of possible command values that has the lowest cost is determined and defined as a selected set of command values. In some circumstances, the MPC-determined command value may be replaced by another transmission ratio command based on override inputs. Minimum and maximum transmission ratios are determined based on the override inputs, and a constrained (or arbitrated) transmission ratio is determined therefrom. The constrained or arbitrated transmission ratio is used to determine whether to apply an MPC-determined transmission ratio or a transmission ratio based on the arbitrated transmission ratio to determine an ultimate commanded transmission ratio. Pressure(s) are commanded to a transmission pulley assembly, which is configured to implement the ultimate commanded transmission ratio.