2020/03/17 by Daniel Arnström, Arnström, Daniel, Daniel Axehill +1 · 2 citations
Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Process Optimization and Integration
paper · pdf · doi:10.48550/arxiv.2003.07605
openalex publication_date 2020/03/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In model predictive control (MPC) an optimization problem has to be solved at\neach time step, which in real-time applications makes it important to solve\nthese optimization problems efficiently and to have good upper bounds on\nworst-case solution time. Often for linear MPC problems, the optimization\nproblem in question is a quadratic program (QP) that depends on parameters such\nas system states and reference signals. A popular class of methods for solving\nsuch QPs is active-set methods, where a sequence of linear systems of equations\nis solved. We propose an algorithm for computing which sequence of subproblems\nan active-set algorithm will solve, for every parameter of interest. By knowing\nthese sequences, a worst-case bound on how many iterations, and ultimately the\nmaximum time, the active-set algorithm requires to converge can be determined.\nThe usefulness of the proposed method is illustrated on a set of QPs,\noriginating from MPC problems, by computing the exact worst-case number of\niterations primal and dual active-set algorithms require to reach optimality.\n