Hybrid Partial And Full Step Quadratic Solver For Model Predictive Control Of Diesel Engine Air Path Flow And Methods Of Use

A method for controlling an internal combustion engine having, within an air path of the engine, a variable geometry turbine (VGT), an exhaust gas recirculation (EGR) valve, and an EGR throttle, the method comprising:

• formulating a constrained optimization problem for a model predictive control (MPC) controller controlling the air path based on a linear model, one or more constraints, and associated dual space and primal space matrix arrays, the linear model comprising a convex, quadratic, time-varying cost function in dual and primal space, and each array associated with a unique active set list comprising a first combination of the one or more constraints;
• solving the constrained optimization problem to determine a solution;
• updating the constrained optimization problem with an updated active set list;
• repeating the solving and formulating steps until all possible active set lists of the one or more constraints are satisfied to generate a requested optimized VGT lift and a requested optimized EGR valve flow rate, each of which meets the one or more constraints, to control the air path, wherein:
• the requested optimized VGT lift responsive to an engine intake manifold pressure is generated by controlling the VGT, and
• the requested optimized EGR valve flow rate responsive to an EGR rate is generated by controlling the EGR valve and the EGR throttle;
• and
• implementing the solution with respect to the air path.

A system for controlling an internal combustion engine having, within an air path of the engine, a variable geometry turbine (VGT), an exhaust gas recirculation (EGR) valve, and an EGR throttle, the system comprising:

• a processor communicatively coupled to a non-transitory computer storage medium, wherein the non-transitory computer storage medium stores instructions that, when executed by the processor, cause the processor to:
• formulate a constrained optimization problem for a model predictive control (MPC) controller controlling the air path based on a linear model, one or more constraints, and associated dual space and primal space matrix arrays, the linear model comprising a convex, quadratic, time-varying cost function in dual and primal space, and each array associated with a unique active set list comprising a first combination of the one or more constraints;
• solve the constrained optimization problem to determine a solution;
• update the constrained optimization problem with an updated active set list;
• repeat the solving and formulating steps until all possible active set lists of the one or more constraints are satisfied to generate a requested optimized VGT lift and a requested optimized EGR valve flow rate, each of which meets the one or more constraints, to control the air path, wherein:
• the requested optimized VGT lift responsive to an engine intake manifold pressure is generated by controlling the VGT, and
• the requested optimized EGR valve flow rate responsive to an EGR rate is generated by controlling the EGR valve and the EGR throttle;
• and implement the solution with respect to the air path.