Sufficient Conditions for Convergent Recursive Extrapolation of qLPV Scheduling Parameters Along a Prediction Horizon
Marcelo Menezes Morato, Julio E. Normey‐Rico, Olivier Sename
Abstract
Model predictive control (MPC) algorithms have long been applied to nonlinear processes. In a quasi-linear parameter varying (qLPV) setting, nonlinearities are included into bounded scheduling parameters, which are given as a function of endogenous variables; these scheduling parameters are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> unknown along a future prediction horizon, which complicates MPC design. To address this problem, the literature points out two options: robust MPC approaches, considering the scheduling to be uncertain; or suboptimal ones that set values for these parameters along the horizon. With respect to the latter group, this article proposes an extrapolation algorithm that estimates the future values of the qLPV scheduling parameters for a fixed prediction horizon of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> steps; the method is based on a recursive procedure using simple Taylor expansions. Sufficient conditions for convergent extrapolation are presented with regard to the form and class of the scheduling function and the robustness of the MPC. Different benchmark examples from the literature are presented to illustrate the algorithm, which is also compared to state-of-the-art techniques.