On the Choice of the Cost Function for Nonlinear Model Predictive Control: A Multi-criteria Evaluation.

Typically, Model Predictive Control (MPC) algorithms minimise the sum of squared predicted control errors, i.e., the L $$_2$$ norm. This work reviews the possible cost functions that may be used in MPC. Eight different cost functions are considered and their usefulness is investigated. For a neutralisation reactor benchmark, the influence of the cost function on the resulting control quality is compared in terms of as many as eight indices. All studied approaches are compared in two scenarios: with no process disturbances and when measurement noise and a disturbance affect the process.