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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:
    Frames and factorization of graph Laplacians
    Autorzy:
    Jorgensen, P.
    Tian, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255936.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    unbounded operators
    deficiency-indices
    Hilbert space
    boundary values
    weighted graph
    reproducing kernel
    Dirichlet form
    graph Laplacian
    resistance network
    harmonic analysis
    frame
    Parseval frame
    Friedrichs extension
    reversible random walk
    resistance distance
    energy Hilbert space
    Opis:
    Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space [formula] of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in [formula] we characterize the Priedrichs extension of the [formula]-graph Laplacian. We consider infinite connected network-graphs G = (V, E), V for vertices, and E for edges. To every conductance function c on the edges E of G, there is an associated pair [formula] where [formula] in an energy Hilbert space, and Δ (=Δc) is the c-graph Laplacian; both depending on the choice of conductance function c. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in [formula] consisting of dipoles. Now Δ is a well-defined semibounded Hermitian operator in both of the Hilbert [formula] and [formula]. It is known to automatically be essentially selfadjoint as an [formula]-operator, but generally not as an [formula] operator. Hence as an [formula] operator it has a Friedrichs extension. In this paper we offer two results for the Priedrichs extension: a characterization and a factorization. The latter is via [formula].
    Źródło:
    Opuscula Mathematica; 2015, 35, 3; 293-332
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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