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  • 1.
    Ceragioli, Francesca
    et al.
    Politécnico di Torino, Dip. di Mathematica.
    Lindmark, Gustav
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Veibäck, Clas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Wahlström, Niklas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Lindfors, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A bounded confidence model that preserves the signs of the opinions2016In: Proceedings of the 2016 European Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 543-548Conference paper (Refereed)
    Abstract [en]

    The aim of this paper is to suggest a modification to the usual bounded confidence model of opinion dynamics, so that “changes of opinion” (intended as changes of the sign of the initial state) of an agent are never induced by the dynamics. In order to do so, a bipartite consensus model is used, endowing it with a confidence range. The resulting signed bounded confidence model has a state-dependent connectivity and a behavior similar to its standard counterpart, but in addition it preserves the sign of the opinions by “repelling away” opinions localized near the origin but on different sides with respect to 0.

  • 2.
    Lindmark, Gustav
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Methods and algorithms for control input placement in complex networks2018Licentiate 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”.

    List of papers
    1. Controllability of complex networks with unilateral inputs
    Open this publication in new window or tab >>Controllability of complex networks with unilateral inputs
    2017 (English)In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 1824Article in journal (Refereed) Published
    Abstract [en]

    In this paper, we study the problem of controlling complex networks with unilateral controls, i.e., controls which can assume only positive or negative values, not both. Given a complex network represented by the adjacency matrix A, an algorithm is developed that constructs an input matrix B such that the resulting system (A, B) is controllable with a near minimal number of unilateral control inputs. This is made possible by a reformulation of classical conditions for controllability that casts the minimal unilateral input selection problem into well known optimization problems. We identify network properties that make unilateral controllability relatively easy to achieve as compared to unrestricted controllability. The analysis of the network topology for instance allows us to establish theoretical bounds on the minimal number of controls required. For various categories of random networks as well as for a number of real-world networks these lower bounds are often achieved by our heuristics.

    Place, publisher, year, edition, pages
    NATURE PUBLISHING GROUP, 2017
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-138253 (URN)10.1038/s41598-017-01846-6 (DOI)000401262400017 ()28500342 (PubMedID)
    Available from: 2017-06-13 Created: 2017-06-13 Last updated: 2019-07-05
    2. Minimum energy control for complex networks
    Open this publication in new window or tab >>Minimum energy control for complex networks
    2018 (English)In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 8, article id 3188Article in journal (Refereed) Published
    Abstract [en]

    The aim of this paper is to shed light on the problem of controlling a complex network with minimal control energy. We show first that the control energy depends on the time constant 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 complete controllability. In the limit case of networks having all purely imaginary eigenvalues (e.g. networks of coupled harmonic oscillators), several constructive algorithms for minimum control energy driver node selection are developed. A general heuristic principle valid for any directed network is also proposed: the overall cost of controlling a network is reduced when the controls are concentrated on the nodes with highest ratio of weighted outdegree vs indegree.

    Place, publisher, year, edition, pages
    NATURE PUBLISHING GROUP, 2018
    National Category
    Other Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-145766 (URN)10.1038/s41598-018-21398-7 (DOI)000425285200018 ()29453421 (PubMedID)
    Note

    Funding Agencies|Swedish Research Council [2015-04390]

    Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2019-07-05
  • 3.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A driver node selection strategy for minimizing the control energy in complex networks2017In: IFAC PAPERSONLINE, ELSEVIER SCIENCE BV , 2017, Vol. 50, no 1, p. 8309-8314Conference paper (Refereed)
    Abstract [en]

    \This paper deals with the problem of controlling linear complex networks in an efficient way, i.e., with limited control energy. A general principle is provided, based on the eigenvalues of the network. It is shown numerically that the cost of controlling a network grows with the (absolute value of the) real part of the eigenvalues of the adjacency matrix. Constructive rules for driver node selection are also provided, based on the (weighted) topology of the network. In particular, we show that the key to have an energetically efficient driver node placement strategy is to use the skewness of the outdegree versus indegree distributions of the network, a topological property not associated before to controllability. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

  • 4.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Combining centrality measures for control energy reduction in network controllability problems2019In: Proceedings of the 2019 European Control Conference (ECC), Institute of Electrical and Electronics Engineers (IEEE), 2019, p. 1518-1523Conference 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.

  • 5.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Controllability of complex networks with unilateral inputs2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 1824Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the problem of controlling complex networks with unilateral controls, i.e., controls which can assume only positive or negative values, not both. Given a complex network represented by the adjacency matrix A, an algorithm is developed that constructs an input matrix B such that the resulting system (A, B) is controllable with a near minimal number of unilateral control inputs. This is made possible by a reformulation of classical conditions for controllability that casts the minimal unilateral input selection problem into well known optimization problems. We identify network properties that make unilateral controllability relatively easy to achieve as compared to unrestricted controllability. The analysis of the network topology for instance allows us to establish theoretical bounds on the minimal number of controls required. For various categories of random networks as well as for a number of real-world networks these lower bounds are often achieved by our heuristics.

  • 6.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Minimum energy control for complex networks2018In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 8, article id 3188Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to shed light on the problem of controlling a complex network with minimal control energy. We show first that the control energy depends on the time constant 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 complete controllability. In the limit case of networks having all purely imaginary eigenvalues (e.g. networks of coupled harmonic oscillators), several constructive algorithms for minimum control energy driver node selection are developed. A general heuristic principle valid for any directed network is also proposed: the overall cost of controlling a network is reduced when the controls are concentrated on the nodes with highest ratio of weighted outdegree vs indegree.

  • 7.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Minimum energy control for networks of coupled harmonic oscillators2017In: IFAC PAPERSONLINE, ELSEVIER SCIENCE BV , 2017, Vol. 50, no 1, p. 8321-8326Conference paper (Refereed)
    Abstract [en]

    The aim of this paper is to investigate the problem of selecting driver nodes enabling the control of a network with minimal control energy. The networks we are interested in are coupled harmonic oscillators, i.e., networks in which the eigenvalues are all purely imaginary. For them, several criteria for driver node selection are presented, based on the different measures of control energy considered in this context. The constructive algorithms we develop for these criteria are normally solving the problem in a heuristic way, although in one case the exact solution can be computed efficiently regardless of size. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

  • 8.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Positive Controllability of Large-Scale Networks2016In: Proceedings of the 2016 European Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 819-824Conference 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.

  • 9.
    Lindmark, Gustav
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Topological aspects of controlling large scale networks with unilateral inputs2017In: IFAC PAPERSONLINE, ELSEVIER SCIENCE BV , 2017, Vol. 50, no 1, p. 8315-8320Conference paper (Refereed)
    Abstract [en]

    In this paper, we study the problem of controlling complex networks with unilateral controls, i.e., controls which can assume only positive or negative values, not both. Given a network with linear dynamics represented by the adjacency matrix A, we seek to understand the minimal number of unilateral controls that renders the network controllable. This problem has structural properties that for instance allows us to establish theoretical bounds and identify key topological properties that makes a network relatively easy to control with unilateral controls as compared to unrestricted controls. We find that the structure of the left null space of A is particularly important to this end. In a computational study we find that the network topology largely determines the number of unilateral controls and that the derived lower bounds often are achieved with heuristic methods. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

1 - 9 of 9
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