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Distributed Semidefinite Programming With Application to Large-Scale System Analysis
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Tech Univ Denmark, Denmark.
Lund Univ, Sweden.
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 4, p. 1045-1058Article in journal (Refereed) Published
Abstract [en]

Distributed algorithms for solving coupled semidefinite programs commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper, we show that in case the coupled problem has an inherent tree structure, it is possible to devise an efficient distributed algorithm for solving such problems. The proposed algorithm relies on predictor- corrector primal-dual interior-point methods, where we use a message-passing algorithm to compute the search directions distributedly. Message passing here is closely related to dynamic programming over trees. This allows us to compute the exact search directions in a finite number of steps. This is because computing the search directions requires a recursion over the tree structure and, hence, terminates after an upward and downward pass through the tree. Furthermore, this number can be computed a priori and only depends on the coupling structure of the problem. We use the proposed algorithm for analyzing robustness of large-scale uncertain systems distributedly. We test the performance of this algorithm using numerical examples.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 63, no 4, p. 1045-1058
Keywords [en]
Distributed algorithms; interconnected uncertain systems; primal-dual methods; robustness analysis; semidefinite programs (SDPs)
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147388DOI: 10.1109/TAC.2017.2739644ISI: 000429056000010OAI: oai:DiVA.org:liu-147388DiVA, id: diva2:1206725
Note

Funding Agencies|Swedish Department of Education within the ELLIIT project; Swedish Research Council [2012-5357]

Available from: 2018-05-17 Created: 2018-05-17 Last updated: 2018-05-17

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CiteExportLink to record
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  • apa
  • harvard1
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  • Other style
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Language
  • de-DE
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  • sv-SE
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