A system according to the present disclosure includes a model predictive control (MPC) module and an actuator module. The MPC module generates a set of possible target values for an actuator of an engine and predicts an operating parameter for the set of possible target values. The predicted operating parameter includes an emission level and/or an operating parameter of an exhaust system. The MPC module determines a cost for the set of possible target values and selects the set of possible target values from multiple sets of possible target values based on the cost. The MPC module determines whether the predicted operating parameter for the selected set satisfies a constraint and sets target values to the possible target values of the selected set when the predicted operating parameter satisfies the constraint. The actuator module controls an actuator of an engine based on at least one of the target values.