Coordination in multiagent systems and Laplacian spectra of digraphs

Abstract

Abstract-Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results published earlier to decentralized control and touch upon some problems of spectral graph theory.

Recurrent approximation as the tool for expansion of functions and modes of operation of neural network

“…As demonstrated in papers [11,[18][19][20], the application of recurrent network for the initial data processing creates preconditions and realizes the advantages of a comprehensive approach to the processes of collection, initial processing, accumulation of data, searching for mathematical models, formation of knowledge bases. Development of the structure of such networks, search for and application of convolutions leads to the creation of hybrid and recurrent networks [23].…”

“…The introduction of indicators [16,18], which are formed by the comparative rules, demonstrates that they can be used for the formation of productive rules. Development of the systems for initial processing of data using RANN [16,18], that has recently been implemented in the automated systems [7][8][9], in industries [12][13][14] that are rapidly readjusted, and surveillance systems [14], necessitates further development of rapid methods [19][20][21][22] of instantaneous learning and qualitative analysis and the methods of formation of results -conclusions based on it [7,8,10,[19][20][21][22]. As demonstrated in articles [15][16][17], new types of representation of continuous signal with a simultaneous application of the indicators -vectors [16] and recurrent approximation [15] opens new approaches to diagnosing [15,16] and creation of RANN.…”

An overview of consensus problems in constrained multi-agent coordination

“…For more details * Corresponding author. Email: hjgao@hit.edu.cn and progress reports, see the survey papers (Cao, Yu, Ren, & Chen, 2013;Chebotarev & Agaev, 2009;Leonard et al, 2007;Olfati-Saber, Fax, & Murray, 2007;Ren, Beard, & Atkins, 2007;Zhang, Gao, & Kaynak, 2013), the books (Bai, Arcak, & Wen, 2011;Gazi & Fidan, 2007;Mesbahi & Egerstedt, 2010;Qu, 2009;Ren & Beard, 2008;Shamma, 2007;Wu, 2007) and references therein.…”

The projection method for continuous-time consensus seeking

“…A necessary and sufficient condition of this is [1] the presence of a spanning in-tree in the dependency digraph. If this condition is satisfied, then consensus can be expressed [2][3][4] by the inner product of the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix and the vector of initial opinions. In [5,6], it was found that for an arbitrary dependency digraph, the limiting state vector of the above protocol is equal to the product of the eigenprojection of the Laplacian matrix, L, and the vector of initial opinions.…”