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Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems
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.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Lund University, Sweden.
2011 (English)Report (Other academic)
Abstract [en]

We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected systems. To facilitate distributed implementation of robust stability analysis of such systems, we propose two algorithms based on decomposition and simultaneous projections. The first algorithm is a nonlinear variant of Cimmino’s mean projection algorithm, but by taking the structure of the constraints into account, we can obtain a faster rate of convergence. The second algorithm is devised by applying the alternating direction method of multipliers to a convex minimization reformulation of the convex feasibility problem. We use numerical results to show that both algorithms require far less iterations than the accelerated nonlinear Cimmino algorithm.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. , 24 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3033
Keyword [en]
Robust stability analysis, Convex feasibility problems, Projection algorithms, Decomposition, Distributed computing
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-72209ISRN: LiTH-ISYR- 3033OAI: oai:DiVA.org:liu-72209DiVA: diva2:458302
Funder
eLLIIT - The Linköping‐Lund Initiative on IT and Mobile Communications
Available from: 2011-11-22 Created: 2011-11-22 Last updated: 2014-09-01Bibliographically approved
In thesis
1. Topics in Robustness Analysis
Open this publication in new window or tab >>Topics in Robustness Analysis
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, we investigate two problems in robustness analysis of uncertain systems with structured uncertainty. The first problem concerns the robust finite frequency range H2 analysis of such systems. Classical robust H2 analysis methods are based on upper bounds for the robust H2 norm of a system which are computed over the whole frequency range. These bounds can be overly conservative, and therefore, classical robust H2 analysis methods can produce misleading results for finite frequency range analysis. In the first paper in the thesis, we address this issue by providing two methods for computing upper bounds for the robust finite-frequency H2 norm of the system. These methods utilize finitefrequency Gramians and frequency partitioning to calculate upper bounds for the robust finite-frequency H2 norm of uncertain systems with structured uncertainty. We show the effectiveness of these algorithms using both theoretical and practical experiments.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. 27 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1512
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-72210 (URN)LiU-TEK-LIC-2011:51 (Local ID)978-91-7393-014-7 (ISBN)LiU-TEK-LIC-2011:51 (Archive number)LiU-TEK-LIC-2011:51 (OAI)
Presentation
2011-12-02, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2011-11-22 Created: 2011-11-22 Last updated: 2011-11-22Bibliographically approved

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Khoshfetrat Pakazad, SinaAndersen, Martin S.Hansson, Anders

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CiteExportLink to record
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Citation style
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