Model Predictive Control Systems And Methods For Increasing Computational Efficiency

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 performs multiple iterations to determine a current set of target values based on the second torque request, a model of the engine, a tableau matrix, and a basic solution matrix, wherein each of the iterations includes the MPC module:
• determining whether the basic solution matrix is:
• not in standard form including a non-basic pair of primal and dual variables;
• or in standard form including a basic pair of primal and dual variables;
• when the basic solution matrix is not in standard form, identifying a first column of the tableau matrix based on a first entry position of the primal variable of the non-basic pair;
• when the basic solution matrix is in standard form and one or more primal variables of the basic solution matrix are negative, identifying the first column of the tableau matrix based on a second entry position of a dual variable of the basic pair;
• and
• selectively updating the basic solution matrix based on the first column of the tableau matrix;
• and
• an actuator module that controls an engine actuator based on a first one of the current set of target values.