Adaptive bipartite consensus for dynamic event-triggered multi-agent systems under DoS attacks

Xiaoli Ruan; Zhiwei Du; Huali Yang; Chen Wang; Jianwen Feng; Xiaoli Ruan; Zhiwei Du; Huali Yang; Chen Wang; Jianwen Feng

doi:10.3934/math.20261016

AIMS Mathematics

2026, Volume 11, Issue 8: 25295-25321. doi: 10.3934/math.20261016

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Adaptive bipartite consensus for dynamic event-triggered multi-agent systems under DoS attacks

1.
School of Computer Science and Aritificial Intelligence, Wuhan Textile University, Wuhan, China
2.
School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, China

Received: 12 June 2026 Revised: 31 July 2026 Accepted: 04 August 2026 Published: 17 August 2026
MSC : 93C27

This paper studies the leader-following bipartite consensus issue for multi-agent systems (MASs) with event-triggered control strategy under denial-of-service (DoS) attacks. To prevent parameters from growing unboundedly during the adaptive process, a projection operator-based adaptive control algorithm combined with a distributed dynamic event-triggered (DET) control strategy is introduced. This control strategy can also reduce unnecessary communication burden. Unlike most existing control algorithms for structurally balanced graphs, a partition algorithm is used to achieve bipartite consensus for the structurally unbalanced case. Besides, by utilizing LMI technology and the Lyapunov function method, several criteria are established to guarantee the stability of error systems under DoS attacks. Moreover, a proof by contradiction is employed to rule out Zeno behavior. Finally, the effectiveness and superiority of the proposed approach are verified by a simulation example.
- event-triggered control,
- multi-agent systems,
- bipartite consensus,
- Zeno behavior
Citation: Xiaoli Ruan, Zhiwei Du, Huali Yang, Chen Wang, Jianwen Feng. Adaptive bipartite consensus for dynamic event-triggered multi-agent systems under DoS attacks[J]. AIMS Mathematics, 2026, 11(8): 25295-25321. doi: 10.3934/math.20261016

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Abstract

This paper studies the leader-following bipartite consensus issue for multi-agent systems (MASs) with event-triggered control strategy under denial-of-service (DoS) attacks. To prevent parameters from growing unboundedly during the adaptive process, a projection operator-based adaptive control algorithm combined with a distributed dynamic event-triggered (DET) control strategy is introduced. This control strategy can also reduce unnecessary communication burden. Unlike most existing control algorithms for structurally balanced graphs, a partition algorithm is used to achieve bipartite consensus for the structurally unbalanced case. Besides, by utilizing LMI technology and the Lyapunov function method, several criteria are established to guarantee the stability of error systems under DoS attacks. Moreover, a proof by contradiction is employed to rule out Zeno behavior. Finally, the effectiveness and superiority of the proposed approach are verified by a simulation example.

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