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<p>This paper tackles the event-triggered approximate optimal consensus problem for nonlinear multi-agent systems (MASs) in the presence of denial of service (DoS) attacks. To begin, the stochastic nature of attack times and durations is considered, and the attacked systems are modeled as 2-mode Markovian switched multi-agent systems (2M-MS-MASs), incorporating both attack and dormant modes. Based on this model, consensus conditions for the switched system are derived. Next, an event-triggered approximate optimal control strategy is proposed, which satisfies the Hamilton–Jacobi–Bellman (HJB) equation and captures the Markovian switched characteristics. To determine the optimal strategy, an approximate dynamic programming (ADP) algorithm is introduced, which is implemented using a neural network with a critic-actor architecture, where weight estimation is achieved through gradient descent. Finally, the proposed approach is validated through two illustrative examples, demonstrating its effectiveness.</p>

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Event-triggered approximate optimal consensus for multi-agent systems under stochastic DoS attacks

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Lei Li,
  • Lei Liu,
  • Dongmei Yan,
  • Jinde Cao,
  • Liang Hua

摘要

This paper tackles the event-triggered approximate optimal consensus problem for nonlinear multi-agent systems (MASs) in the presence of denial of service (DoS) attacks. To begin, the stochastic nature of attack times and durations is considered, and the attacked systems are modeled as 2-mode Markovian switched multi-agent systems (2M-MS-MASs), incorporating both attack and dormant modes. Based on this model, consensus conditions for the switched system are derived. Next, an event-triggered approximate optimal control strategy is proposed, which satisfies the Hamilton–Jacobi–Bellman (HJB) equation and captures the Markovian switched characteristics. To determine the optimal strategy, an approximate dynamic programming (ADP) algorithm is introduced, which is implemented using a neural network with a critic-actor architecture, where weight estimation is achieved through gradient descent. Finally, the proposed approach is validated through two illustrative examples, demonstrating its effectiveness.