Consensus in Networks of Multiagents with Switching Topologies Modeled as Adapted Stochastic Processes

  • Authors:

  • Bo Liu;Wenlian Lu;Tianping Chen

  • Affiliations:

  • 071018024@fudan.edu.cn;wenlian@fudan.edu.cn;tchen@fudan.edu.cn

  • Venue:
  • SIAM Journal on Control and Optimization
  • Year:
  • 2011

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Abstract

In this paper, we discuss the consensus problem in networks of multiagents with stochastically switching topologies. The switch of graph topology is modeled as an adapted stochastic process, which in principle can include any stochastic processes such as independent and identically distributed (i.i.d.) processes and Markov chains. We derive the sufficient conditions for consensus in both discrete-time and continuous-time networks in terms of conditional expectations of the underlying graph topology. We prove that if there exist $T0$ and $\delta0$ such that the conditional expectation of the union of the $\delta$-graph topologies across each $T$-length time interval has spanning trees, then the multiagent system reaches consensus. For comparison, we show that some previous results on this topic can be derived from our main theorem as corollaries. This includes important results when the switching topology can be modeled as the special and important stochastic models—the i.i.d. process and the Markov process—which implies that we generalize the previous results to some extent. As applications, we also give some corollaries concerning stochastic processes other than the i.i.d. process and Markov processes, such as independent but not necessarily identically distributed processes, hidden Markov models, and $\phi$-mixing processes.