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Distributed Resilient Asymmetric Bipartite Consensus: A Data-Driven Event-Triggered Mechanism

Yi Zhang, Mohamadamin Rajabinezhad, Shan Zuo

TL;DR

This work tackles leader–follower consensus in nonlinear discrete-time multi-agent systems with asymmetric (positive/negative) interactions under aperiodic Denial-of-Service attacks. It introduces a data-driven event-triggered (DDET) framework that adapts a time-varying parameter and computes a neighborhood ABC error without requiring explicit system models. By leveraging asymmetric gains $m$ and $n$, a CFDL data model, and a DoS-robust triggering rule, the approach achieves bounded leader–follower tracking errors while reducing communication. Numerical examples with constant and time-varying leader references demonstrate the method’s resilience to data losses and its practical efficacy in nonlinear networked settings. The proposed DDET protocol offers a scalable, model-free path to resilient ABC in complex cyber-physical networks where communication is unreliable.

Abstract

The problem of asymmetric bipartite consensus control is investigated within the context of nonlinear, discrete-time, networked multi-agent systems (MAS) subject to aperiodic denial-of-service (DoS) attacks. To address the challenges posed by these aperiodic DoS attacks, a data-driven event-triggered (DDET) mechanism has been developed. This mechanism is specifically designed to synchronize the states of the follower agents with the leader's state, even in the face of aperiodic communication disruptions and data losses. Given the constraints of unavailable agents' states and data packet loss during these attacks, the DDET control framework resiliently achieves leader-follower consensus. The effectiveness of the proposed framework is validated through two numerical examples, which showcase its ability to adeptly handle the complexities arising from aperiodic DoS attacks in nonlinear MAS settings.

Distributed Resilient Asymmetric Bipartite Consensus: A Data-Driven Event-Triggered Mechanism

TL;DR

This work tackles leader–follower consensus in nonlinear discrete-time multi-agent systems with asymmetric (positive/negative) interactions under aperiodic Denial-of-Service attacks. It introduces a data-driven event-triggered (DDET) framework that adapts a time-varying parameter and computes a neighborhood ABC error without requiring explicit system models. By leveraging asymmetric gains and , a CFDL data model, and a DoS-robust triggering rule, the approach achieves bounded leader–follower tracking errors while reducing communication. Numerical examples with constant and time-varying leader references demonstrate the method’s resilience to data losses and its practical efficacy in nonlinear networked settings. The proposed DDET protocol offers a scalable, model-free path to resilient ABC in complex cyber-physical networks where communication is unreliable.

Abstract

The problem of asymmetric bipartite consensus control is investigated within the context of nonlinear, discrete-time, networked multi-agent systems (MAS) subject to aperiodic denial-of-service (DoS) attacks. To address the challenges posed by these aperiodic DoS attacks, a data-driven event-triggered (DDET) mechanism has been developed. This mechanism is specifically designed to synchronize the states of the follower agents with the leader's state, even in the face of aperiodic communication disruptions and data losses. Given the constraints of unavailable agents' states and data packet loss during these attacks, the DDET control framework resiliently achieves leader-follower consensus. The effectiveness of the proposed framework is validated through two numerical examples, which showcase its ability to adeptly handle the complexities arising from aperiodic DoS attacks in nonlinear MAS settings.

Paper Structure

This paper contains 8 sections, 4 theorems, 23 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. System Modeling and Problem Formulation
  4. DDET Algorithm Design
  5. Numerical Example
  6. DDET under Aperiodic DoS with Constant Leader
  7. DDET under Aperiodic DoS with Time-Varing Leader
  8. CONCLUSION

Key Result

Lemma 1

For nonlinear systems eq3 satisfying the Assumptions ass:1 and ass:3, there exists a time-varying parameter called pseudo partial derivative (PPD) $\mathscr{M}_{i}^y(k) \in \mathbb{R}$ such that the systems eq3 can be equivalently transformed into the following compact-form dynamic linearization (CF where $\left|\mathscr{M}_i^y(k)\right| \leqslant b_i^y$ is bounded with $\forall k$ and $i \in \mat

Figures (3)

  • Figure 1: The structurally balanced, signed, directed communication graph for networked agents.
  • Figure 2: (a) The grey line is reference leader $y_d$, the red line is the desired trajectory of $\mathcal{V}_1$, and the yellow line is the desired trajectory of $\mathcal{V}_2$. (b) Output trajectories under the DDET protocols without aperiodic DoS attacks: The gray solid line represents the constant leader reference signal $y_d(k)$. (c) Output trajectories $y_i(k)$ under Aperiodic DoS attacks while using the DDET protocols: The gray solid line represents the constant leader reference signal $y_d(k)$. (d) The event-triggered function value $g_i\left(\Delta_{i}(k), \tilde{e}_{y_i}(k)\right)$ based on the developed data-driven parameter while under aperiodic DoS attacks.
  • Figure 3: (a) The grey line is reference leader $y_d$, the red line is the desired trajectory of $\mathcal{V}_1$, and the yellow line is the desired trajectory of $\mathcal{V}_2$. (b) Output trajectories under the DDET protocols without aperiodic DoS attacks: The gray solid line represents the constant leader reference signal $y_d(k)$. (c) Output trajectories under the DDET protocols under aperiodic DoS attacks: The gray solid line represents the constant leader reference signal $y_d(k)$. (d) The event-triggered function value $g_i\left(\Delta_{i}(k), \tilde{e}_{y_i}(k)\right)$ based on the developed data-driven parameter while under aperiodic DoS attacks.

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Remark 1
  • Remark 2
  • Lemma 1: hou2010novel
  • Definition 3
  • Remark 3
  • Lemma 2: zhang2024resilient
  • Lemma 3: ma2021distributed
  • Remark 4
  • ...and 2 more