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Event triggered optimal formation control for nonlinear multi-agent systems under Denial-of-Service attacks

Jianqiang Zhang, Kaijun Yang

TL;DR

This work addresses formation control for nonlinear multi-agent systems operating under Denial-of-Service (DoS) attacks with limited communication. It introduces an event-triggered, critic-network-based approach to approximate the coupled Hamilton-Jacobi-Bellman equations and derive distributed optimal policies, analyzed via Lyapunov methods to guarantee exponential convergence under DoS bounds. The key contributions include a DoS-resilient, single-network critic-ADP scheme, explicit bounds on attack frequency and length ensuring stability, and a non-Zeno, communication-efficient triggering mechanism validated by MATLAB simulations. The proposed method reduces communication load while maintaining robust formation performance, illustrating practical resilience of MASs in adversarial networks.

Abstract

This paper investigates the optimal formation control problem of a class of nonlinear multi-agent systems(MASs) under Denial-of-Service(DoS) attacks. We design the optimal formation control law using an event-triggered control scheme to achieve formation objectives under DoS attacks. Critic neural network (NN)-based approach is employed to achieve the optimal control policy under DoS attacks. Event-triggered mechanism is introduced to ensure the saving of control resources. Additionally, Lyapunov stability theory is utilized to demonstrate that the local neighborhood formation error exhibits exponential stability and the estimation error of weights are uniformly ultimately bounded. Finally, the effectiveness of the control algorithm is validated through matlab simulations. The results indicate that under DoS attacks, the nonlinear MAS successfully achieves the desired formation for the MAS.

Event triggered optimal formation control for nonlinear multi-agent systems under Denial-of-Service attacks

TL;DR

This work addresses formation control for nonlinear multi-agent systems operating under Denial-of-Service (DoS) attacks with limited communication. It introduces an event-triggered, critic-network-based approach to approximate the coupled Hamilton-Jacobi-Bellman equations and derive distributed optimal policies, analyzed via Lyapunov methods to guarantee exponential convergence under DoS bounds. The key contributions include a DoS-resilient, single-network critic-ADP scheme, explicit bounds on attack frequency and length ensuring stability, and a non-Zeno, communication-efficient triggering mechanism validated by MATLAB simulations. The proposed method reduces communication load while maintaining robust formation performance, illustrating practical resilience of MASs in adversarial networks.

Abstract

This paper investigates the optimal formation control problem of a class of nonlinear multi-agent systems(MASs) under Denial-of-Service(DoS) attacks. We design the optimal formation control law using an event-triggered control scheme to achieve formation objectives under DoS attacks. Critic neural network (NN)-based approach is employed to achieve the optimal control policy under DoS attacks. Event-triggered mechanism is introduced to ensure the saving of control resources. Additionally, Lyapunov stability theory is utilized to demonstrate that the local neighborhood formation error exhibits exponential stability and the estimation error of weights are uniformly ultimately bounded. Finally, the effectiveness of the control algorithm is validated through matlab simulations. The results indicate that under DoS attacks, the nonlinear MAS successfully achieves the desired formation for the MAS.

Paper Structure

This paper contains 12 sections, 3 theorems, 70 equations, 10 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM STATEMENT AND PRELIMINARIES
  3. Graph theory
  4. Problem formulation
  5. DoS attack model
  6. Event-triggered Optimal Controller Design
  7. Stability Analysis
  8. Policy Iteration (PI) Algorithm for Coupled HJB Equations
  9. Approximate Solutions of Coupled HJB Equations using NNs
  10. Simulation
  11. Simulation for MAS with formation control
  12. Conclusion

Key Result

theorem 1

Consider the nonlinear MAS xuhao1 and xuhao2. Suppose that Assumptions Assu1 - Assu2 hold, by designing the event-triggering condition $g(t)=$ If the system satisfies the DoS attack frequency $F(0,t)\le \frac{{{k}^{*}}}{\ln ({\zeta{C}_{4}})}$ and the DoS attack length rate $T<\frac{{{C}_{1}}-{{k}^{*}}}{{{C}_{1}}+{{C}_{2}}}$, $\zeta$, ${k}^{*}$, ${C}_{2}$ and ${C}_{4}$ are positive constants to be

Figures (10)

  • Figure 1: Formation tracking controller for the $i$th follower
  • Figure 2: The communication topology of the MASs.
  • Figure 3: The trajectory of the Multi-agent systems.
  • Figure 4: Formation tracking error in horizontal direction.
  • Figure 5: Formation tracking error in vertical direction.
  • ...and 5 more figures

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • remark 1
  • theorem 1
  • proof 1
  • remark 2
  • theorem 2
  • proof 2
  • theorem 3
  • proof 3
  • ...and 1 more