Group pinning consensus under fixed and randomly
switching topologies with acyclic partition

Yilun Shang; Yilun Shang

doi:10.3934/nhm.2014.9.553

Networks and Heterogeneous Media

2014, Volume 9, Issue 3: 553-573. doi: 10.3934/nhm.2014.9.553

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Group pinning consensus under fixed and randomly switching topologies with acyclic partition

Yilun Shang ^{1
,}

1.
Department of Mathematics, Tongji University, Shanghai 200092

Received: 01 December 2013 Revised: 01 June 2014
Primary: 93C05, 37H10, 05C20; Secondary: 05C50, 60J27.

This paper addresses group consensus problems in generic linear multi-agent systems with directed information flow over (i) fixed topology and (ii) randomly switching topology governed by a continuous-time homogeneous Markov process. We propose two types of pinning control protocols to ensure group consensus regardless of the magnitude of the coupling strengths among the agents. In the case of randomly switching topology, we show that the group consensus behavior is unrelated to the magnitude of the couplings among agents if the union of the topologies corresponding to the positive recurrent states of the Markov process possesses an acyclic partition. Sufficient conditions for achieving group consensus are presented in terms of simple graphic conditions, which are easy to be checked compared to conventional algebraic criteria. Simulation examples are also presented to validate the effectiveness of the theoretical results.
- Network of multi-agents,
- pinning control,
- linear time-invariant system,
- Markovian switching,
- directed acyclic graph
Citation: Yilun Shang. Group pinning consensus under fixed and randomlyswitching topologies with acyclic partition[J]. Networks and Heterogeneous Media, 2014, 9(3): 553-573. doi: 10.3934/nhm.2014.9.553

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Abstract

This paper addresses group consensus problems in generic linear multi-agent systems with directed information flow over (i) fixed topology and (ii) randomly switching topology governed by a continuous-time homogeneous Markov process. We propose two types of pinning control protocols to ensure group consensus regardless of the magnitude of the coupling strengths among the agents. In the case of randomly switching topology, we show that the group consensus behavior is unrelated to the magnitude of the couplings among agents if the union of the topologies corresponding to the positive recurrent states of the Markov process possesses an acyclic partition. Sufficient conditions for achieving group consensus are presented in terms of simple graphic conditions, which are easy to be checked compared to conventional algebraic criteria. Simulation examples are also presented to validate the effectiveness of the theoretical results.

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