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Decentralized design of consensus protocols with minimal communication links based on directed spanning tree

Yangzhou Chen, Lanhao Zhao

Abstract

This paper proposes a decentralized design approach of consensus protocols of multi-agent systems via a directed-spanning-tree(DST)-based linear transformation and the corresponding minimal communication links. First, the consensus problem of multi-agent systems is transformed into the decentralized output stabilization problem by constructing a linear transformation based on a DST of the communication topology, and thus a necessary and sufficient consensus criterion in terms of decentralized fixed mode is derived. Next, a new distributed protocol is designed by using only the neighbors information on the DST, which is a fully decentralized design approach. Finally, some numerical examples are given to verify the results attained.

Decentralized design of consensus protocols with minimal communication links based on directed spanning tree

Abstract

This paper proposes a decentralized design approach of consensus protocols of multi-agent systems via a directed-spanning-tree(DST)-based linear transformation and the corresponding minimal communication links. First, the consensus problem of multi-agent systems is transformed into the decentralized output stabilization problem by constructing a linear transformation based on a DST of the communication topology, and thus a necessary and sufficient consensus criterion in terms of decentralized fixed mode is derived. Next, a new distributed protocol is designed by using only the neighbors information on the DST, which is a fully decentralized design approach. Finally, some numerical examples are given to verify the results attained.
Paper Structure (5 sections, 5 theorems, 45 equations, 8 figures)

This paper contains 5 sections, 5 theorems, 45 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Problem description and transformation
  3. Decentralized consensus protocol design via minimal communication links
  4. Numerical examples
  5. Conclusion

Key Result

Lemma 1

Any edge state $x_{j i}, i \in V, j \in N_i$ can be linearly represented by the fundamental edge states $y_i=x_{k_i}-x_i,i=1, \cdots, N-1$ on the DST.

Figures (8)

  • Figure 1: The communication topology of Example 1
  • Figure 2: The first components of the states
  • Figure 3: The second components of the states
  • Figure 4: The communication topology of Example 2.
  • Figure 5: The first components of the states
  • ...and 3 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Definition 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Theorem 3