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Reaching Resilient Leader-Follower Consensus in Time-Varying Networks via Multi-Hop Relays

Liwei Yuan, Hideaki Ishii

TL;DR

The objective is to develop distributed algorithms for the nonfaulty/normal followers to track an arbitrary reference value propagated by a set of leaders while they are in interaction with the unknown adversarial agents.

Abstract

We study resilient leader-follower consensus of multi-agent systems (MASs) in the presence of adversarial agents, where agents' communication is modeled by time-varying topologies. The objective is to develop distributed algorithms for the nonfaulty/normal followers to track an arbitrary reference value propagated by a set of leaders while they are in interaction with the unknown adversarial agents. Our approaches are based on the weighted mean subsequence reduced (W-MSR) algorithms with agents being capable to communicate with multi-hop neighbors. Our algorithms can handle agents possessing first-order and second-order dynamics. Moreover, we characterize necessary and sufficient graph conditions for our algorithms to succeed by the novel notion of jointly robust following graphs. Our graph condition is tighter than the sufficient conditions in the literature when agents use only one-hop communication (without relays). Using multi-hop relays, we can enhance robustness of leader-follower networks without increasing communication links and obtain further relaxed graph requirements for our algorithms to succeed. Numerical examples are given to verify the efficacy of our algorithms.

Reaching Resilient Leader-Follower Consensus in Time-Varying Networks via Multi-Hop Relays

TL;DR

The objective is to develop distributed algorithms for the nonfaulty/normal followers to track an arbitrary reference value propagated by a set of leaders while they are in interaction with the unknown adversarial agents.

Abstract

We study resilient leader-follower consensus of multi-agent systems (MASs) in the presence of adversarial agents, where agents' communication is modeled by time-varying topologies. The objective is to develop distributed algorithms for the nonfaulty/normal followers to track an arbitrary reference value propagated by a set of leaders while they are in interaction with the unknown adversarial agents. Our approaches are based on the weighted mean subsequence reduced (W-MSR) algorithms with agents being capable to communicate with multi-hop neighbors. Our algorithms can handle agents possessing first-order and second-order dynamics. Moreover, we characterize necessary and sufficient graph conditions for our algorithms to succeed by the novel notion of jointly robust following graphs. Our graph condition is tighter than the sufficient conditions in the literature when agents use only one-hop communication (without relays). Using multi-hop relays, we can enhance robustness of leader-follower networks without increasing communication links and obtain further relaxed graph requirements for our algorithms to succeed. Numerical examples are given to verify the efficacy of our algorithms.

Paper Structure

This paper contains 17 sections, 7 theorems, 41 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Settings
  3. Graph Notions
  4. System Model and Algorithm
  5. Threat Model
  6. Jointly Robust Following Graphs
  7. Jointly r-Reachable Followers with l Hops
  8. Jointly r-Robust Following Graphs with l Hops
  9. Resilient Leader-Follower Consensus in First-Order MASs
  10. Convergence Analysis
  11. Analysis on Secure Leader Agents and Comparisons with Related Works
  12. Properties of Jointly (f+1)-Robust Following Graphs
  13. Resilient Leader-Follower Consensus in Second-Order MASs
  14. Numerical Examples
  15. Simulation in A Time-Varying First-Order MAS
  16. ...and 2 more sections

Key Result

Lemma 1

Consider the time-varying network $\mathcal{G}[k] = (\mathcal{V},\mathcal{E}[k])$ with $l$-hop communication, where each normal follower node $i\in \mathcal{W}^\mathcal{N}$ updates its value according to the MW-MSR algorithm with parameter $f$. Under the $f$-local adversarial set $\mathcal{A}$ and t

Figures (9)

  • Figure 1: The graph $\mathcal{G}[k]$ is not a jointly 2-robust following graph with 1 hop but is a jointly 2-robust following graph with 2 hops under the 1-local model. The set of leader agents $\mathcal{L}$ is {7, 8, 9}.
  • Figure 2: The graph $\mathcal{G}[k]$ is a jointly 2-robust following graph with 1 hop under the 1-local model. The set of leader agents $\mathcal{L}$ is {7, 8, 9}.
  • Figure 3: The graph $\mathcal{G}[k]$ is not a jointly 3-robust following graph with 1 hop but is a jointly 3-robust following graph with 3 hops under the 2-local model. The set of leader agents $\mathcal{L}$ is {11, 12, 13, 14, 15}.
  • Figure 4: Nodes' values in the time-varying leader-follower network in Fig. \ref{['15node']} applying the MW-MSR algorithm.
  • Figure 5: Normal nodes track the time-varying reference value in the time-varying leader-follower network in Fig. \ref{['15node']} using the three-hop MW-MSR algorithm.
  • ...and 4 more figures

Theorems & Definitions (28)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Example 1
  • Example 2
  • Definition 6
  • Remark 1
  • Definition 7
  • ...and 18 more