Average consensus on general strongly connected digraphs

  • Authors:
  • Kai Cai;Hideaki Ishii

  • Affiliations:
  • Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, Ontario M5S 3G4, Canada;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-J2-54, Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2012

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Abstract

We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two linear distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. In both cases, the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs; in particular, this graphical condition does not require that the network be balanced or symmetric, thereby extending previous results in the literature. The key novelty of our approach is to augment an additional variable for each agent, called ''surplus'', whose function is to locally record individual state updates. For convergence analysis, we employ graph-theoretic and nonnegative matrix tools, plus the eigenvalue perturbation theory playing a crucial role.