On the Robustness of Receding Horizon Control using Nonlinear Approximated Models

This paper investigates the robustness of Nonlinear Model Predictive Control (NMPC) laws that employ approximated models, derived with Nonlinear Set Membership (NSM) techniques, with bounded model uncertainty. Although theoretical results already exist in the literature for the robustness analysis and for the robust design of NMPC in the face of a given description and related bound of the model uncertainty, the issue of how to practically estimate such an uncertainty bound is still an open one. This work shows that, with the proposed NSM approach, measured process input/output data can be employed to derive directly an input/output model and a bound of the related model uncertainty. The obtained uncertainty bound can be then employed to evaluate the effects of model uncertainty on the closed loop system performance. Moreover, since the NSM approach is able to provide an input/output model with minimal uncertainty bound, it is shown that improved robustness of the closed loop system can be obtained, with respect to that of a NMPC law based on a physical model. The effectiveness of the proposed approach is shown in a vehicle lateral stability control problem, through numerical simulations of harsh maneuvers using a detailed nonlinear vehicle model.