Asymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies

Authors:
G. Yin;Yu Sun;Le Yi Wang
Affiliations:
Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, United States
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate parameter @e0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a stepsize @m that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, we show that when 0