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  • 1.
    Bernard, Florian
    et al.
    MPI Informatics, Saarland Informatics Campus, Saarbrücken, Germany.
    Thunberg, Johan
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Goncalves, Jorge
    LCSB, University of Luxembourg, Esch-sur-Alzette, Luxembourg.
    Theobalt, Christian
    MPI Informatics, Saarland Informatics Campus, Saarbrücken, Germany.
    Synchronisation of partial multi-matchings via non-negative factorisations2019In: Pattern Recognition, ISSN 0031-3203, E-ISSN 1873-5142, Vol. 92, p. 146-155Article in journal (Refereed)
    Abstract [en]

    In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equal to the identity. Motivated by clustering and matrix factorisation perspectives of cycle-consistency, we derive an algo- rithm to tackle the permutation synchronisation problem based on non-negative factorisations. In order to deal with the inherent non-convexity of the permutation synchronisation problem, we use an initialisation procedure based on a novel rotation scheme applied to the solution of the spectral relaxation. Moreover, this rotation scheme facilitates a convenient Euclidean projection to obtain a binary solution after solving our relaxed problem. In contrast to state-of-the-art methods, our approach is guaranteed to produce cycle-consistent results. We experimentally demonstrate the efficacy of our method and show that it achieves better results compared to existing methods. © 2019 Elsevier Ltd

  • 2.
    Markdahl, Johan
    et al.
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg, Luxembourg.
    Thunberg, Johan
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Gonçalves, Jorge
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg, Luxembourg.
    Towards Almost Global Synchronization on the Stiefel Manifold2018In: 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, Dec. 17-19, 2018, Miami Beach, Florida: IEEE, 2018, p. 496-501Conference paper (Refereed)
    Abstract [en]

    The Kuramoto model evolves on the circle, i.e., the 1-sphere S1. A graph G is referred to as S1 -synchronizing if the Kuramoto model on G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are Sn -synchronizing for all n ≥ 2. However, that does not hold for = 1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St(1, n+1). As such, it is natural to ask for the extent to which the results on Sn can be extended to the Stiefel manifold. This paper shows that all connected graphs are St(p, n) -synchronizing provided the pair (p, n) satisfies p ≤ [2n/3]-1. © Copyright 2019 IEEE - All rights reserved.

  • 3.
    Thunberg, Johan
    et al.
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Lyamin, Nikita
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Sjöberg, Katrin
    Scania, Södertälje, Sweden.
    Vinel, Alexey
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES). Department of Electrical Engineering, Western Norway University of Applied Sciences, Bergen, Norway.
    Vehicle-to-Vehicle Communications for Platooning: Safety Analysis2019In: IEEE Networking Letters, ISSN 2576-3156, Vol. 1, no 4, p. 168-172Article in journal (Refereed)
    Abstract [en]

    Vehicle-to-vehicle (V2V) communication is the key technology enabling platooning. This paper proposes an analytical framework that combines the characteristics of V2V communication (packet loss probabilities and packet transmission delays) with the physical mobility characteristics of vehicles (speed, distance between vehicles and their brake capacities). First, we present the feasible region of communications delays which guarantees safe emergency braking in platooning scenarios. Second, we derive a bound on the probability of safe braking. The presented framework is applied to understand the performance of the state-of-the-art V2V communication protocol for platooning.

  • 4.
    Thunberg, Johan
    et al.
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
    Markdahl, Johan
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
    Bernard, Florian
    Max-Planck-Institute for Informatics, Saarland Informatics Campus, Germany.
    Goncalves, Jorge
    Systems Biomedicine, University of Luxembourg, Luxembourg.
    A lifting method for analyzing distributed synchronization on the unit sphere2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 96, p. 253-258Article in journal (Refereed)
    Abstract [en]

    This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence.

  • 5.
    Thunberg, Johan
    et al.
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Markdahl, Johan
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
    Goncalves, Jorge
    Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
    Dynamic controllers for column synchronization of rotation matrices: A QR-factorization approach2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, p. 20-25Article in journal (Refereed)
    Abstract [en]

    In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d−1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d−k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.

  • 6.
    Wei, Jieqiang
    et al.
    ACCESS Linnaeus Centre School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden.
    Zhang, Silun
    School of Engineering Sciences, KTH Royal Institute of Technology, Stockholm, Sweden..
    Adaldo, Antonio
    ACCESS Linnaeus Centre School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden.
    Thunberg, Johan
    Halmstad University, School of Information Technology. Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg.
    Hu, Xiaoming
    Division of Optimization and Systems Theory Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden.
    Johansson, Karl Henrik
    ACCESS Linnaeus Centre School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden.
    Finite-Time Attitude Synchronization With Distributed Discontinuous Protocols2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 10, p. 3608-3615Article in journal (Refereed)
    Abstract [en]

    The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and nonsmooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper. 

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