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An ADMM Algorithm for Solving l(1) Regularized MPC
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-1927-1690
2012 (English)In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, 4486-4491 p.Conference paper (Refereed)
Abstract [en]

We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an ℓ1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in ℓ1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, and enables separation of the optimization problem into sub-problems that may be solved in parallel. We show that the most costly step of the proposed ADMM algorithm is equivalent to solving an LQ regulator problem with an extra linear term in the cost function, a problem that can be solved efficiently using a Riccati recursion. We apply the ADMM algorithm to an example of ℓ1 regularized MPC. The numerical examples confirm fast convergence to sufficient accuracy and a linear complexity in the MPC prediction horizon.

Place, publisher, year, edition, pages
IEEE , 2012. 4486-4491 p.
, IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Keyword [en]
Algorithm for solving, Alternating direction method of multipliers, Equality constraints, Fast convergence, In-control, Least-squares cost functions, Linear complexity, Linear terms, LQ regulators, Numerical example, Optimization problems, Prediction horizon, Riccati recursion, Sub-problems
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-118908DOI: 10.1109/CDC.2012.6426429ISI: 000327200404132ScopusID: 2-s2.0-84874275663ISBN: 978-1-4673-2066-5OAI: diva2:609056
51st IEEE Conference on Decision and Control, CDC 2012; Maui, HI; United States; 10 December 2012 through 13 December 2012

QC 20130304

Available from: 2013-03-04 Created: 2013-03-04 Last updated: 2013-12-19Bibliographically approved

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