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Resilient Multi-Dimensional Consensus and Distributed Optimization against Agent-Based and Denial-of-Service Attacks

Hongjian Chen, Changyun Wen, Xiaolei Li

TL;DR

This work tackles resilient coordination in multi-agent systems by addressing both agent-based faults and edge-targeted DoS attacks. It introduces an auxiliary-point algorithm with a safe kernel to ensure consensus within the convex hull of benign initial states, even when communication is intermittently blocked. The RMDO extension combines a subgradient step with the resilient consensus to guarantee asymptotic convergence to the global optimizer under distributed, redundantcost structures. Theoretical analyses leveraging $r$-robustness, objective redundancy, and Sarymsakov matrices are complemented by numerical examples demonstrating practical robustness and performance gains.

Abstract

In this paper, we consider the resilient multi-dimensional consensus and distributed optimization problems of multi-agent systems (MASs) in the presence of both agent-based and denial-of-service (DoS) attacks. The considered agent-based attacks can cover malicious, Byzantine, and stubborn agents. The links between agents in the network can be blocked by DoS attacks, which may lead the digraph to be time-varying and even disconnected. The objective is to ensure that the remaining benign agents achieve consensus. To this end, an "auxiliary point"-based resilient control algorithm is proposed for MASs. Under the proposed algorithm, each healthy agent constructs a "safe kernel" utilizing the states of its in-neighbors and updates its state toward a specific point within this kernel at each iteration. If an agent cannot receive its neighbors' states owing to DoS attacks, it will use the states received immediately before the DoS period. Moreover, a resilient multi-dimensional distributed optimization (RMDO) algorithm is also proposed. Theoretical proofs and numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.

Resilient Multi-Dimensional Consensus and Distributed Optimization against Agent-Based and Denial-of-Service Attacks

TL;DR

This work tackles resilient coordination in multi-agent systems by addressing both agent-based faults and edge-targeted DoS attacks. It introduces an auxiliary-point algorithm with a safe kernel to ensure consensus within the convex hull of benign initial states, even when communication is intermittently blocked. The RMDO extension combines a subgradient step with the resilient consensus to guarantee asymptotic convergence to the global optimizer under distributed, redundantcost structures. Theoretical analyses leveraging -robustness, objective redundancy, and Sarymsakov matrices are complemented by numerical examples demonstrating practical robustness and performance gains.

Abstract

In this paper, we consider the resilient multi-dimensional consensus and distributed optimization problems of multi-agent systems (MASs) in the presence of both agent-based and denial-of-service (DoS) attacks. The considered agent-based attacks can cover malicious, Byzantine, and stubborn agents. The links between agents in the network can be blocked by DoS attacks, which may lead the digraph to be time-varying and even disconnected. The objective is to ensure that the remaining benign agents achieve consensus. To this end, an "auxiliary point"-based resilient control algorithm is proposed for MASs. Under the proposed algorithm, each healthy agent constructs a "safe kernel" utilizing the states of its in-neighbors and updates its state toward a specific point within this kernel at each iteration. If an agent cannot receive its neighbors' states owing to DoS attacks, it will use the states received immediately before the DoS period. Moreover, a resilient multi-dimensional distributed optimization (RMDO) algorithm is also proposed. Theoretical proofs and numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.

Paper Structure

This paper contains 21 sections, 8 theorems, 54 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph theory
  4. Objective redundancy
  5. Sarymsakov matrix
  6. Problem formulation
  7. Problem formulation
  8. Agent-based attacks
  9. DoS attacks
  10. Resilient consensus problem
  11. RMDO problem
  12. A resilient consensus algorithm
  13. Algorithm design
  14. Performance analysis
  15. Resilient multi-dimensional distributed optimization
  16. ...and 6 more sections

Key Result

Lemma 1

zhu2023resilient For any subset $\mathcal{V}_1 \subsetneq \mathcal{V}$ with $|\mathcal{V}_1| \textcolor{rgb(170,0,0)}{\geq} N-r$, if an MAS consisting of $N$ agents is $r$-redundant, then it holds that

Figures (9)

  • Figure 1: An explanation of the former discussion and (\ref{['no of B vanish']}).
  • Figure 2: An explanation of time duration $\xi_\eta$, where the red area denoted the finite DoS attacks time between $t_k$ and $t_\eta$. $|\mathcal{B}|$ represents the effective updating steps.
  • Figure 3: An explanation of time duration between $t_k$ and $t_{\iota\eta}$, where the red area denotes the independent finite DoS attacks time satisfying Assumption \ref{['DoS-duration']}. There is no requirement for general intervals to have consistent length.
  • Figure 4: Communication network
  • Figure 5: Types of DoS Attacks
  • ...and 4 more figures

Theorems & Definitions (29)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • Definition 4
  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 5
  • Definition 6
  • ...and 19 more