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Lindmark, G. & Altafini, C. (2019). Combining centrality measures for control energy reduction in network controllability problems. In: Proceedings of the 2019 European Control Conference (ECC): . Paper presented at European Control Conference (ECC) 2019, June 25-28, Naples, Italy (pp. 1518-1523). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Combining centrality measures for control energy reduction in network controllability problems
2019 (English)In: Proceedings of the 2019 European Control Conference (ECC), Institute of Electrical and Electronics Engineers (IEEE), 2019, p. 1518-1523Conference paper, Published paper (Refereed)
Abstract [en]

This paper investigates the problem of controlling a complex network with reduced control energy. Two centrality measures are defined, one related to the energy that a control, placed on a node, can exert on the entire network, and the other related to the energy that the network exerts on a node. We show that by combining these two centrality measures conflicting control energy requirements, like minimizing the average energy needed to steer the state in any direction and the energy needed for the worst direction, can be simultaneously taken into account. From an algebraic point of view, the node ranking that we obtain from the combination of our centrality measures is related to the non-normality of the adjacency matrix of the graph.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2019
Keywords
Control over networks, Large-scale systems, Network analysis and control
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-158607 (URN)10.23919/ECC.2019.8795867 (DOI)9783907144008 (ISBN)9783907144015 (ISBN)9781728113142 (ISBN)
Conference
European Control Conference (ECC) 2019, June 25-28, Naples, Italy
Available from: 2019-07-05 Created: 2019-07-05 Last updated: 2019-08-19Bibliographically approved
Lindmark, G. (2018). Methods and algorithms for control input placement in complex networks. (Licentiate dissertation). Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Methods and algorithms for control input placement in complex networks
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The control-theoretic notion of controllability captures the ability to guide a systems behavior toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. brings many opportunities. It could for instance enable improved efficiency in the functioning of a network or lead to that entirely new applicative possibilities emerge. However, when control theory is applied to complex networks like these, several challenges arise. This thesis consider some of these challenges, in particular we investigate how control inputs should be placed in order to render a given network controllable at a minimum cost, taking as cost function either the number of control inputs or the energy that they must exert. We assume that each control input targets only one node (called a driver node) and is either unconstrained or unilateral.

A unilateral control input is one that can assume either positive or negative values but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. We show that the unilateral controllability problem is to a high degree structural and derive theoretical lower bounds on the minimal number of unilateral control inputs from topological properties of the network, similar to the bounds that exists for the minimal number of unconstrained control inputs. Moreover, an algorithm is developed that constructs a near minimal number of control inputs for a given network. When evaluated on various categories of random networks as well as a number of real-world networks, the algorithm often achieves the theoretical lower bounds.

A network can be controllable in theory but not in practice when completely unreasonable amounts of control energy are required to steer it in some direction. For unconstrained control inputs we show that the control energy depends on the time constants of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for control. We also investigate the problem of placing driver nodes such that the control energy requirements are minimized (assuming that theoretical controllability is not an issue). For the special case with networks having all purely imaginary eigenvalues, several constructive algorithms for driver node placement are developed. In order to understand what determines the control energy in the general case with arbitrary eigenvalues, we define two centrality measures for the nodes based on energy flow considerations: the first centrality reflects the network impact of a node and the second the ability to control it indirectly. It turns out that whether a node is suitable as driver node or not largely depends on these two qualities. By combining the centralities into node rankings we obtain driver node placements that significantly reduce the control energy requirements and thereby improve the “practical degree of controllability”.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 36
Series
Linköping Studies in Science and Technology. Licentiate Thesis, ISSN 0280-7971 ; 1814
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-150886 (URN)10.3384/lic.diva-150886 (DOI)9789176852439 (ISBN)
Presentation
2018-08-30, 00:00 (English)
Opponent
Supervisors
Note

Minor corrections are made in the electronic version of the thesis (Abstract). / Mindre korreigeringar är gjorda i den elektroniska versionen av avhandlingen (i Abstract).

Available from: 2018-09-03 Created: 2018-09-03 Last updated: 2019-10-12Bibliographically approved
Lindmark, G. & Altafini, C. (2016). Positive Controllability of Large-Scale Networks. In: Proceedings of the 2016 European Control Conference: . Paper presented at European Control Conference, 2016, Aalborg, Denmark (pp. 819-824). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Positive Controllability of Large-Scale Networks
2016 (English)In: Proceedings of the 2016 European Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 819-824Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we study the problem of controlling large scale networks with controls which can assume only positive values. Given an adjacency matrix A, an algorithm is developed that constructs an input matrix B with a minimal number of columns such that the resulting system (A, B) is positively controllable. The algorithm combines the graphical methods used for structural controllability analysis with the theory of positive linear dependence. The number of control inputs guaranteeing positive controllability is near optimal.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016
Keywords
Complex Networks, Controllability
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-130780 (URN)10.1109/ECC.2016.7810390 (DOI)000392695300137 ()978-1-5090-2591-6 (ISBN)978-1-5090-2592-3 (ISBN)978-1-5090-2590-9 (ISBN)
Conference
European Control Conference, 2016, Aalborg, Denmark
Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2017-08-09
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-4049-6018

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