A System-Theoretic Approach to Construct a Banded Null Basis to Efficiently Solve MPC-Based QP Problems

Jiaheng Yang, T. J. Meijer, V. S. Dolk, Bram de Jager, W. P.M.H. Heemels

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)


The null-space method is able to reduce the number of decision variables in the on-line optimization carried out in model predictive control. This method relies on the construction of a basis for the null space of the equality constraints. This paper proposes a systematic approach based on system-theoretic insights to construct such a basis with a banded structure. This banded structure carries over to the resulting lower-dimensional QP and can be exploited to compute a solution more efficiently. Specifically, solvers that exploit this structure result in a computational complexity that scales linearly with the prediction horizon. In contrast to similar approaches in the literature, the proposed method can be applied to uncontrollable, though stabilizable, systems with multiple inputs. This method is particularly interesting when dealing with systems with large state dimension and long prediction horizons. Finally, the method is applied to a numerical example in combination with both the alternating direction method of multipliers and the accelerated dual gradient projection method to demonstrate its benefits.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781728113982
Publication statusPublished - Dec 2019
Event58th IEEE Conference on Decision and Control (CDC 2019) - Nice, France
Duration: 11 Dec 201913 Dec 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference58th IEEE Conference on Decision and Control (CDC 2019)
Abbreviated titleCDC 2019
Internet address


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