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Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Technical University of Denmark, Lyngby, Denmark.
Lund University, Sweden.
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, 2594-2599 p.Conference paper, Published paper (Refereed)
Abstract [en]

Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.

Place, publisher, year, edition, pages
International Federation of Automatic Control , 2014. 2594-2599 p.
Series
World Congress, ISSN 1474-6670 ; Volume 19, Part 1
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-110127DOI: 10.3182/20140824-6-ZA-1003.01649ISBN: 978-3-902823-62-5 (print)OAI: oai:DiVA.org:liu-110127DiVA: diva2:742972
Conference
19th IFAC world congress, The International Federation of Automatic Control, Cape Town, South Africa, August 24-29, 2014
Available from: 2014-09-03 Created: 2014-09-03 Last updated: 2015-05-19Bibliographically approved
In thesis
1. Divide and Conquer: Distributed Optimization and Robustness Analysis
Open this publication in new window or tab >>Divide and Conquer: Distributed Optimization and Robustness Analysis
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

As control of large-scale complex systems has become more and more prevalent within control, so has the need for analyzing such controlled systems. This is particularly due to the fact that many of the control design approaches tend to neglect intricacies in such systems, e.g., uncertainties, time delays, nonlinearities, so as to simplify the design procedure.

Robustness analysis techniques allow us to assess the effect of such neglected intricacies on performance and stability. Performing robustness analysis commonly requires solving an optimization problem. However, the number of variables of this optimization problem, and hence the computational time, scales badly with the dimension of the system. This limits our ability to analyze large-scale complex systems in a centralized manner. In addition, certain structural constraints, such as privacy requirements or geographical separation, can prevent us from even forming the analysis problem in a centralized manner.

In this thesis, we address these issues by exploiting structures that are common in large-scale systems and/or their corresponding analysis problems. This enables us to reduce the computational cost of solving these problems both in a centralized and distributed manner. In order to facilitate distributed solutions, we employ or design tailored distributed optimization techniques. Particularly, we propose three distributed optimization algorithms for solving the analysis problem, which provide superior convergence and/or computational properties over existing algorithms. Furthermore, these algorithms can also be used for solving general loosely coupled optimization problems that appear in a variety of fields ranging from control, estimation and communication systems to supply chain management and economics.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 330 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1676
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-117503 (URN)10.3384/diss.diva-117503 (DOI)978-91-7519-050-1 (ISBN)
Public defence
2015-06-11, Visionen, Hus B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-05-04 Created: 2015-04-29 Last updated: 2017-01-17Bibliographically approved

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Khoshfetrat Pakazad, SinaHansson, Anders

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