Fast Nonlinear Model Predictive Control via Set Membership Approximation: An Overview

Abstract

The use of Set Membership (SM) function approximation techniques is described, in order to compute off-line a control law $\kappa^\text{SM}$ which approximates a given Nonlinear Model Predictive Control (NMPC) law. The on-line evaluation time of $\kappa^\text{SM}$ is faster than the optimization required by the NMPC receding horizon strategy, thus allowing application of NMPC also on processes with “fast” dynamics. Moreover, SM methodology allows to derive approximated control laws with guaranteed worst-case accuracy, which can be suitably tuned to achieve closed loop stability and performance properties that are arbitrarily close to those of the exact NMPC controller. In particular, the properties of three different SM techniques are reviewed here, namely the “optimal”, “nearest point” and the “local” approximations, and their performances are compared on a numerical example.