A new framework and online solution engines for multiparametric Model Predictive Control

In this paper, we combine the multiparametric programming approach proposed in Pistikopoulos et al., 2002 for quadratic Model Predictive Control (mp-QP/MPC) problems, with the solution strategy proposed in Narciso et al. 2022 for mp-QP problems. The problem statements in these two contributions are fully compatible, and we show firstly how they can be combined to deliver critical regions and the corresponding control laws of MPC problems in the offline stage. Then, a new online architecture is proposed for the calculation of optimal control actions. To this end we explore the convenient solution structure presented in Narciso et al. 2022 with the specific aim to calculate them as fast as possible via parallel processing, and where a restricted collection of critical regions is kept and continuously updated in time.