Model predictive control systems and methods for internal combustion engines

An engine control system for a vehicle, comprising:

• a torque requesting module that generates a first torque request for a spark ignition engine based on driver input;
• a torque conversion module that converts the first torque request into a second torque request;
• a model predictive control (MPC) module that determines a set of target values based on the second torque request, a model of the engine, and a matrix having dimensions of (m+n) by (m+n), where n is an integer greater than zero that is equal to a number of lower boundary constraints used in the determination of the set of target values and m is an integer greater than zero that is equal to a number of constraints used in the determination of the set of target values other than the lower boundary constraints;
• a throttle actuator module that controls opening of a throttle valve based on a first one of the target values;
• a boost actuator module that controls opening of a wastegate of a turbocharger based on a second one of the target values;
• an exhaust gas recirculation (EGR) actuator module that controls opening of an EGR valve based on a third one of the target values;
• and
• a phaser actuator module that controls intake and exhaust valve phasing based on fourth and fifth ones of the target values, respectively.