liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Distributed Semidefinite Programming with Application to Large-scale System Analysis
Linköping University, Department of Electrical Engineering, Automatic Control.
Linköping University, Department of Electrical Engineering, Automatic Control.
Technical University of Denmark. (Applied Mathematics and Computer Science)
Lund University. (Automatic Control)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require manyiterations to converge. They also put high computational demand on the computational agents. In thispaper we show that in case the coupled problem has an inherent tree structure, it is possible to devisean efficient distributed algorithm for solving such problems. This algorithm can potentially enjoy thesame efficiency as centralized solvers that exploit sparsity. The proposed algorithm relies on predictorcorrectorprimal-dual interior-point methods, where we use a message-passing algorithm to compute thesearch directions distributedly. Message-passing here is closely related to dynamic programming overtrees. This allows us to compute the exact search directions in a finite number of steps. Furthermorethis number can be computed a priori and only depends on the coupling structure of the problem. Weuse the proposed algorithm for analyzing robustness of large-scale uncertain systems distributedly. Wetest the performance of this algorithm using numerical examples.

National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-117496OAI: oai:DiVA.org:liu-117496DiVA: diva2:808669
Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2015-05-19
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 (print) (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: 2015-05-19Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Khoshfetrat Pakazad, Sina
By organisation
Automatic Control
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 71 hits
ReferencesLink to record
Permanent link

Direct link