Coordinate-Descent Augmented Lagrangian Methods for Interpretative and Adaptive Model Predictive Control

Model predictive control (MPC) of nonlinear systems suffers a trade-off between model accuracy and real-time compu- tational burden. This thesis presents an interpretative and adaptive MPC (IA-MPC) framework for nonlinear systems, which is related to the widely used approximation method based on successive linearization MPC and Extended Kalman Filtering (SL-MPC-EKF). First, we introduce a solution algo- rithm for linear MPC that is based on the combination of Co- ordinate Descent and Augmented Lagrangian (CDAL) ideas. The CDAL algorithm enjoys three features: (i) it is construction-free, in that it avoids explicitly constructing the quadratic pro-gramming (QP) problem associated with MPC; (ii) is matrix-free, as it avoids multiplications and factorizations of matri-ces; and (iii) is library-free, as it can be simply coded without any library dependency, 90-lines of C-code in our implemen-tation. We specialize the algorithm for both state-space for-mulations of MPC and formulations based on AutoRegres-sive with eXogenous terms models (CDAL-ARX). The thesis also presents a rapid-prototype MPC tool based on the gPROMS platform, in which the qpOASES and CDAL algorithm was integrated. In addition, based on an equivalence between SS-based and ARX-based MPC problems we show,we investigate the relation between the proposed IA-MPC and the classical SL-MPC-EKF method. Finally, we test and show the effectiveness of the proposed IA-MPC frameworkon four typical nonlinear MPC benchmark examples.