Resilient Average Consensus for Second-Order Multi-Agent Systems: Algorithms and Application

FANG Chongrong; HUAN Yuehui; ZHENG Wenzhe; BAO Xianchen; LI Zheng

doi:10.11999/JEIT251155

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FANG Chongrong, HUAN Yuehui, ZHENG Wenzhe, BAO Xianchen, LI Zheng. Resilient Average Consensus for Second-Order Multi-Agent Systems: Algorithms and Application[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251155

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FANG Chongrong, HUAN Yuehui, ZHENG Wenzhe, BAO Xianchen, LI Zheng. Resilient Average Consensus for Second-Order Multi-Agent Systems: Algorithms and Application[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251155

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Resilient Average Consensus for Second-Order Multi-Agent Systems: Algorithms and Application

doi: 10.11999/JEIT251155 cstr: 32379.14.JEIT251155

1.
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University , Shanghai, 200400, China
2.
Zhejiang Guoli Security Technology Co. Ltd., Ningbo, 315000, China

Funds: Pioneer Leading Goose+X R&D Program of Zhejiang (2024SJCZX0003, 2024SJCZX0004)

Accepted Date: 2025-12-31
Rev Recd Date: 2025-12-31

Available Online: 2026-01-15

Abstract

Abstract

Objective Multi-agent systems (MASs) are pivotal for collaborative tasks in dynamic environments, with consensus algorithms serving as a cornerstone for applications like formation control. However, MASs are vulnerable to misbehaviors (e.g., malicious attacks or accidental faults), which can disrupt consensus and compromise system performance. While resilient consensus methods exist for first-order systems, they are inadequate for second-order MASs, where agents’ dynamics involve both position and velocity. This work addresses the gap by developing a resilient average consensus framework for second-order MASs that ensures accurate collaboration under misbehaviors. The primary challenges include distributed error detection and compensating two-dimensional state errors (position and velocity) using one-dimensional acceleration inputs. Methods The study first derives sufficient conditions for second-order average consensus under misbehaviors, leveraging graph theory and Lyapunov stability analysis. The system is modeled as an undirected graph $ \mathcal{G}=(\mathcal{V},\mathcal{E}) $, where agents follow double-integrator dynamics. Two algorithms are proposed: Finite Input-Errors Detection-Compensation (FIDC): For finite control input errors, detection strategies (1 and 2) use two-hop communication information to identify discrepancies in neighbors’ states or control inputs. Compensation Scheme I designs input sequences to satisfy consensus conditions (Corollary 1). Infinite Attack Detection-Compensation (IADC): For infinite errors in control input, velocity, and position, detection strategies are extended to identify falsified data. Compensation Schemes 2 and 3 mitigate errors, while an exponentially decaying error bound isolates persistent attackers. The algorithms are distributed and require no global knowledge. Results and Discussions Simulations on a 10-agent network validate the algorithms’ efficacy. Under FIDC, agents achieve exact average consensus despite finite input errors from malicious and faulty agents (Fig. 5). IADC ensures consensus among normal agents after isolating malicious ones exceeding the error bound (Fig. 6). Experimental evaluations on a multi-robot platform demonstrate resilience against real-world faults (e.g., actuator failures) and attacks (e.g., false data injection). In fault scenarios, FIDC reduces formation center deviation from 180mm to 34mm (Fig. 8). For attacks, IADC isolates malicious robots, allowing normal agents to converge correctly (Fig. 9). Discussions on relaxing Assumption 1 (non-adjacent misbehaving agents) reveal that Detection Strategy 3 and majority voting can handle certain connected malicious topologies (Fig. 3–Fig. 4), though complex cases require further study. Conclusions This work proposes a novel resilient average consensus framework for second-order MASs. Theoretically, sufficient conditions ensure consensus under misbehaviors, while FIDC and IADC algorithms enable distributed detection, compensation, and isolation of errors. Simulations and physical experiments confirm that the methods achieve accurate average consensus against both finite and infinite errors. Future work will explore extensions to directed networks, time-varying topologies, and higher-dimensional systems.
- Second-order multi-agent system,
- resilient consensus,
- attack detection,
- compensation

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References(24)

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