Average-consensus Problem of Multi-agent Systems with Non-uniform and Asymmetric Time-delays

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  • SAKURAMA Kazunori
    Graduate School of Informatics and Engineering, The University of Electro-Communications
  • NAKANO Kazushi
    Graduate School of Informatics and Engineering, The University of Electro-Communications

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Other Title
  • 非一様·非対称な時間遅れをもつマルチエージェントシステムの平均合意問題
  • 非一様・非対称な時間遅れを持つマルチエージェントシステム平均合意問題
  • ヒイチヨウ ヒタイショウ ナ ジカン オクレ オ モツ マルチエージェント システム ヘイキン ゴウイ モンダイ

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This paper deals with consensus problems of networked multi-agent systems with non-uniform and asymmetric time-delays. It has been known that multi-agent systems without time-delays achieve average-consensus, which means that all the states of agents converge to the average of their initial states. However, our target systems do not necessarily achieve average-consensus because of the non-uniform and asymmetric time-delays on the networks. The goal of this paper is to derive the necessary and sufficient condition of the network structures under which these systems achieve average-consensus. First, we derive a conservative quantity and calculate a consensus value, which all the agents converge to. We show that the consensus value depends not only on the structures of the time-delay networks and the initial states of the agents, but also on the initial functions, which define the initial conditions for the time-delay systems. Then, the necessary and sufficient condition for average-consensus is derived, which is represented by the eigenvectors of the delay-transition and the delay-weight Laplacians. These Laplacians are newly introduced in this paper to express the structures of the time-delay networks. Finally, the validity of the analysis results are demonstrated by simulations with six-agent systems.

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