A Quadratic Programming Algorithm Based on Nonnegative Least Squares With Applications to Embedded Model Predictive Control

• Published in: IEEE transactions on automatic control Vol. 61; no. 4; pp. 1111 - 1116
• Main Author: Bemporad, Alberto
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Active set methods; Algorithms; Inequalities; Least squares method; Linear systems; Mathematical analysis; Mathematical models; MATLAB; Matrix decomposition; Model predictive control; Nonnegative least squares; Prediction algorithms; Predictive control; Quadratic programming; model predictive control; quadratic programming; nonnegative least squares; Active set methods
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2459211

This technical note proposes an active set method based on nonnegative least squares (NNLS) to solve strictly convex quadratic programming (QP) problems, such as those that arise in Model Predictive Control (MPC). The main idea is to rephrase the QP problem as a Least Distance Problem (LDP) that is solved via a NNLS reformulation. While the method is rather general for solving strictly convex QP's subject to linear inequality constraints, it is particularly useful for embedded MPC because (i) is very fast, compared to other existing state-of-the-art QP algorithms, (ii) is very simple to code, requiring only basic arithmetic operations for computing LDL T decompositions recursively to solve linear systems of equations, (iii) contrary to iterative methods, provides the solution or recognizes infeasibility in a finite number of steps.