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)

Received Date: 2025-11-01
Accepted Date: 2025-12-31
Rev Recd Date: 2025-12-31

Available Online: 2026-01-15

Abstract

Abstract

Objective Multi-Agent Systems (MASs) are central to collaborative tasks in dynamic environments, and consensus algorithms are essential for applications such as formation control. However, MASs are vulnerable to misbehaviors (e.g., malicious attacks or accidental faults) that disrupt consensus and degrade system performance. Existing resilient consensus methods for first-order systems are insufficient for second-order MASs, where both position and velocity states must be considered. This study develops a resilient average consensus framework for second-order MASs that maintains accurate collaboration under misbehaviors. The main challenges are distributed error detection and compensation for two-dimensional state errors (position and velocity) using one-dimensional acceleration inputs. Methods The study derives sufficient conditions for second-order average consensus under misbehaviors using graph theory and Lyapunov stability analysis. The system is modeled as an undirected graph $ \mathcal{G}=(\mathcal{V},\mathcal{E}) $, and 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 to detect discrepancies in neighbors’ states or control inputs. Compensation Scheme 1 generates input sequences that satisfy the consensus conditions in Corollary 1. Infinite Attack Detection–Compensation (IADC): For infinite errors in control inputs, velocities, and positions, the detection strategies are extended to identify falsified data. Compensation Schemes 2 and 3 reduce the effect of these errors, and an exponentially decaying error bound isolates persistent attackers. The algorithms are fully distributed and require no global information. Results and Discussions Simulations on a 10-agent network demonstrate the effectiveness of the algorithms. Under FIDC, agents reach exact average consensus despite finite input errors caused by malicious or faulty agents (Fig. 3). IADC ensures consensus among normal agents after isolating malicious agents that exceed the error bound (Fig. 4). Experiments on a multi-robot platform confirm resilience to real-world faults (e.g., actuator failures) and attacks (e.g., false data injection). In fault scenarios, FIDC reduces the deviation of the formation center from 180 mm to 34 mm (Fig. 6). Under attacks, IADC isolates malicious robots, allowing normal agents to converge correctly (Fig. 7). Analyses of relaxed Assumption 1 (non-adjacent misbehaving agents) show that Detection Strategy 3 and majority voting address certain connected malicious topologies (Fig. 2), although complex cases need further study. Conclusions This work presents a resilient average consensus framework for second-order MASs. Theoretically, the study provides sufficient conditions for consensus under misbehaviors. The FIDC and IADC algorithms enable distributed detection, compensation, and isolation of errors. Simulations and physical experiments verify that the methods achieve accurate average consensus under both finite and infinite errors. Future research 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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