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Robust stability analysis of sparsely interconnected uncertain systems
Technical University of Denmark, Lyngby, Denmark.
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
Lund University, Sweden.
2014 (engelsk)Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, nr 8, s. 2151-2156Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.

sted, utgiver, år, opplag, sider
IEEE , 2014. Vol. 59, nr 8, s. 2151-2156
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-110125DOI: 10.1109/TAC.2014.2305934ISI: 000342923700012OAI: oai:DiVA.org:liu-110125DiVA, id: diva2:742965
Tilgjengelig fra: 2014-09-03 Laget: 2014-09-03 Sist oppdatert: 2017-12-05bibliografisk kontrollert
Inngår i avhandling
1. Divide and Conquer: Distributed Optimization and Robustness Analysis
Åpne denne publikasjonen i ny fane eller vindu >>Divide and Conquer: Distributed Optimization and Robustness Analysis
2015 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Linköping: Linköping University Electronic Press, 2015. s. 330
Serie
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1676
HSV kategori
Identifikatorer
urn:nbn:se:liu:diva-117503 (URN)10.3384/diss.diva-117503 (DOI)978-91-7519-050-1 (ISBN)
Disputas
2015-06-11, Visionen, Hus B, Campus Valla, Linköping, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2015-05-04 Laget: 2015-04-29 Sist oppdatert: 2019-11-15bibliografisk kontrollert

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