Convergence of NMPC using qLPV embeddings and Taylor extrapolation

Recent works have demonstrated that the computational demand of Nonlinear Model Predictive Control (NMPC) can be alleviated when quasi-Linear Parameter Varying (qLPV) models are used. Yet, a difficulty arises: the future scheduling parameter values are typically unavailable. In Morato et al. (2022), a recursive extrapolation method, based on local Taylor expansions of the qLPV function, is proposed. In this communique, we investigate the convergence of such scheme by applying the analysis procedure originally proposed by Hespe and Werner (2021), w.r.t. the MPC from Cisneros et al. (2016), using an inexact Newton root determination problem. We generate an upper bound for the rate of contraction over samples, considering the scheduling trajectories estimation error. Based on simulation results, we advocate that the Taylor-based qLPV MPC technique from Morato et al. (2022) is indeed a highly competitive NMPC solution: similar to state-of-the-art solvers, with relieved numerical complexity (one QP per sample).