A system according to the principles of the present disclosure includes a first model predictive control (MPC) module and an engine actuator module. The first MPC module generates predicted parameters based on a model of an engine and a set of possible target values and generates a cost for the set of possible target values based on the predicted parameters and a desired exhaust enthalpy. The first MPC module also selects the set of possible target values from multiple sets of possible target values based on the cost. The engine actuator module adjusts an actuator of the engine based on at least one of the target values.