Towards proper assessment of QP algorithms for embedded model predictive control

With model predictive control (MPC) becoming a viable approach for advanced feedback control at very fast sampling times, a plethora of methods for solving quadratic programming (QP) problems on embedded computing hardware has been proposed. While most of these methods seem to be useful and superior to competing approaches on particular problem instances, very little effort has been put into a proper benchmarking on a non-trivial number of MPC problems. This paper is intended to help filling this gap by (i) briefly discussing the most important aspects for assessing the suitability of a certain QP method for an MPC problem at hand, (ii) providing a concise overview of about a dozen different QP algorithms that have been proposed for use in MPC, (iii) describing a general benchmarking framework for comparing the numerical performance of the different QP algorithms, and (iv) providing preliminary benchmarking results based on different performance metrics. Numerical performance of the various algorithms is assessed by means of a suitable collection of benchmark problems, taken from both academic studies and industrial applications of MPC.