MPC with conditional penalty cost

Model predictive control (MPC) applications habitually focus on large systems with slow dynamics. In addition, traditional constrained optimization techniques make use of algorithms not suited for fast MPC execution. This work suggests the use of conditional penalties in the optimization cost function to account for constraints. Such penalty functions resemble the barrier functions, where the penalty is always present and increases as the system variables approach a constraint. However, the penalty is considered conditional because it impacts the cost function only when the operating point is found within a tolerance of the constraint limit. Moreover, the constraint penalties and tolerances can be adjusted based on their physical importance relative to the cost weights. This efficient optimization algorithm was successfully tested in an air-heater pilot plant. The fact that constraints are accounted for in the cost function evaluation and the controller calculation is recursive make this technique attractive for fast dynamic systems control applications.