Beyond the quadratic norm: Computationally efficient constrained nonlinear MPC using a custom cost function

A new approach to nonlinear Model Predictive Control (MPC) is discussed in this work. A custom user-defined cost function is used in place of the typically considered quadratic norm. An approximator of the cost function is applied to obtain a computationally simple procedure and linearization of two trajectories is carried out online. The predicted output trajectory of the approximator and the predicted trajectory of the manipulated variable, both over the prediction horizon, are repeatedly linearized online. It yields a simple quadratic programming task. The algorithm is implemented for a simulated neutralization benchmark modeled by a neural Wiener model. The resulting control quality is excellent, identical to that observed in the MPC scheme with nonlinear optimization. Validity of the described MPC algorithms is demonstrated when only simple box constraints are considered on the process input variable and in a more demanding case when additional soft limitations are put on the predicted output. Two structures of the approximator are compared: polynomial and neural; the advantages of the latter one are shown and stressed.