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Byzantine-Resilient Output Optimization of Multiagent via Self-Triggered Hybrid Detection Approach

Chenhang Yan, Liping Yan, Yuezu Lv, Bolei Dong, Yuanqing Xia

TL;DR

A framework aimed at realizing resilient optimization for continuous-time systems by incorporating a novel self-triggered hybrid detection approach that is able to identify attacks on neighbors using both error thresholds and triggering intervals, thereby optimizing the balance between effective attack detection and the reduction of excessive communication triggers.

Abstract

How to achieve precise distributed optimization despite unknown attacks, especially the Byzantine attacks, is one of the critical challenges for multiagent systems. This paper addresses a distributed resilient optimization for linear heterogeneous multi-agent systems faced with adversarial threats. We establish a framework aimed at realizing resilient optimization for continuous-time systems by incorporating a novel self-triggered hybrid detection approach. The proposed hybrid detection approach is able to identify attacks on neighbors using both error thresholds and triggering intervals, thereby optimizing the balance between effective attack detection and the reduction of excessive communication triggers. Through using an edge-based adaptive self-triggered approach, each agent can receive its neighbors' information and determine whether these information is valid. If any neighbor prove invalid, each normal agent will isolate that neighbor by disconnecting communication along that specific edge. Importantly, our adaptive algorithm guarantees the accuracy of the optimization solution even when an agent is isolated by its neighbors.

Byzantine-Resilient Output Optimization of Multiagent via Self-Triggered Hybrid Detection Approach

TL;DR

A framework aimed at realizing resilient optimization for continuous-time systems by incorporating a novel self-triggered hybrid detection approach that is able to identify attacks on neighbors using both error thresholds and triggering intervals, thereby optimizing the balance between effective attack detection and the reduction of excessive communication triggers.

Abstract

How to achieve precise distributed optimization despite unknown attacks, especially the Byzantine attacks, is one of the critical challenges for multiagent systems. This paper addresses a distributed resilient optimization for linear heterogeneous multi-agent systems faced with adversarial threats. We establish a framework aimed at realizing resilient optimization for continuous-time systems by incorporating a novel self-triggered hybrid detection approach. The proposed hybrid detection approach is able to identify attacks on neighbors using both error thresholds and triggering intervals, thereby optimizing the balance between effective attack detection and the reduction of excessive communication triggers. Through using an edge-based adaptive self-triggered approach, each agent can receive its neighbors' information and determine whether these information is valid. If any neighbor prove invalid, each normal agent will isolate that neighbor by disconnecting communication along that specific edge. Importantly, our adaptive algorithm guarantees the accuracy of the optimization solution even when an agent is isolated by its neighbors.

Paper Structure

This paper contains 22 sections, 9 theorems, 55 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works and Motivations
  3. Contributions and Organization
  4. Preliminaries
  5. Graph Theory and Supporting Lemmas
  6. Attack Model
  7. Problem Formulation
  8. Edge-based Event-triggered Adaptive Distributed Optimization Algorithm
  9. Hybrid Adaptive Event-Triggered Protocol
  10. Description of Activation Function
  11. Attack Detection and Isolation
  12. $\mathit{r}$-Isolatable Graph
  13. Attack Detection and Isolation Mechanism
  14. Convergence analysis
  15. Convergence of Optimal Observer
  16. ...and 7 more sections

Key Result

Lemma 1

li2013distributed For an undirected graph $\mathcal{G}$, if it is connected, then all eigenvalues of $L$ have nonnegative real parts, and $0$ is the only zero eigenvalue, corresponding to the right eigenvector $\mathbf{1}$. The smallest positive eigenvalue $\lambda _2$ of $L$ is given by $\lambda _2

Figures (9)

  • Figure 1: Self-triggered detection-based control approach for the HMASs.
  • Figure 2: (a) $1$-isolatable graph. (b) $2$-isolatable graph.
  • Figure 3: Information of launching the attack in a trigger interval.
  • Figure 4: Curves of $\delta_i$ in 0-80 s.
  • Figure 5: Triggering instants of the edges among normal agents.
  • ...and 4 more figures

Theorems & Definitions (23)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 4
  • Remark 1
  • Remark 2
  • Definition 4
  • ...and 13 more