Nonlinear MPC Design using the qLPV Approach and IQC-based Terminal Ingredients

Abstract The design of stabilizing model predictive control laws for systems subject to nonlinearities is often handled using sector arguments. Recent advances have demonstrated that the synthesis of terminal ingredients based on integral quadratic constraints (IQCs) with general dynamic multipliers yields less conservative design—with larger corresponding regions of attraction. However, the resulting predictive control scheme involves a nonlinear prediction model and, hence, may become computationally demanding. Yet, a large body of research has shown that for (quasi-)linear parameter varying (qLPV/LPV) models, which constitute a particular class of nonlinear systems, a significant reduction of the resulting computational burden is possible. Accordingly, in this paper, we provide a systematic nonlinear MPC design procedure combining IQC-based terminal ingredient (for larger stability regions) and LPV tools (for reduced computational load). The proposed scheme is compared, in simulation, to state-of-the-art (nonlinear) MPC algorithms, indicating good control performance with lower associated numerical cost. Moreover, a real processor-in-the-loop validation experiment is provided to demonstrate the applicability of the scheme in practical engineering contexts.