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    Wyświetlanie 1-3 z 3
    Tytuł:
    A generalization of the graph Laplacian with application to a distributed consensus algorithm
    Autorzy:
    Zhai, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/331278.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    graph Laplacian
    generalized graph Laplacian
    adjacency weights
    distributed consensus algorithm
    cooperative control
    Opis:
    In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 2; 353-360
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A matrix inequality based design method for consensus problems in multi-agent systems
    Autorzy:
    Zhai, G.
    Okuno, S.
    Imae, J.
    Kobayashi, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/930012.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system wieloagentowy
    konsensus
    sterowanie zdecentralizowane
    nierówność macierzy
    LMI
    multi-agent systems
    consensus
    decentralized control
    graph Laplacian
    matrix inequality
    Opis:
    In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 4; 639-646
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constrained spectral clustering via multi-layer graph embeddings on a Grassmann manifold
    Autorzy:
    Trokicić, Aleksandar
    Todorović, Branimir
    Powiązania:
    https://bibliotekanauki.pl/articles/329780.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    spectral clustering
    constrained clustering
    multilayer graph
    Grassmann manifold
    Nyström method
    Laplacian matrix
    grupowanie widmowe
    graf wielowarstwowy
    metoda Nyströma
    macierz Laplaciana
    Opis:
    We present two algorithms in which constrained spectral clustering is implemented as unconstrained spectral clustering on a multi-layer graph where constraints are represented as graph layers. By using the Nystrom approximation in one of the algorithms, we obtain time and memory complexities which are linear in the number of data points regardless of the number of constraints. Our algorithms achieve superior or comparative accuracy on real world data sets, compared with the existing state-of-the-art solutions. However, the complexity of these algorithms is squared with the number of vertices, while our technique, based on the Nyström approximation method, has linear time complexity. The proposed algorithms efficiently use both soft and hard constraints since the time complexity of the algorithms does not depend on the size of the set of constraints.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 1; 125-137
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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