Integrator resetting with guaranteed feasibility for an LMI-based robust model predictive control approach

Robust model predictive control (RMPC) formulations are aimed at ensuring stability and constraint satisfaction in the presence of model uncertainties. In this context, the use of linear matrix inequalities (LMI) has become a popular approach. The present work is concerned with the inclusion of integral action in an LMI-based RMPC formulation for the purpose of ensuring offset-free regulation. More specifically, this paper proposes a novel integrator resetting scheme aimed at improving the transient response of the closed-loop system. The resetting procedure is designed to retain the recursive feasibility and asymptotic stability properties of the RMPC formulation. For illustration, simulated examples involving a two-mass-spring system and a simplified helicopter model are presented. The results show that the proposed scheme provides an improvement of the transient response in terms of both overshoot and settling time.