基于输出掩码的合作竞争多智能体系统二分一致性隐私保护问题研究
Privacy-Preserving Bipartite Consensus with Cooperative-Competitive Multi-Agent Interactions: An Output Mask Approach
摘要: 本文研究了连续时间合作-竞争多智能体系统的隐私保护二分一致性问题。为了避免泄露网络节点的初始状态，同时实现具有合作- 竞争的网络节点的二分一致性，本文提出了一种新的基于隐私保护二分一致性控制算法。本文所采用的隐私保护方法为构造一个输出掩码，使智能体的内部状态不被其他智能体察觉。这与现有的差分隐私以及同态加密的隐私保护方法不同，并且创新性地使用在合作- 竞争多智能体系统中。基于所提出的隐私保护算法，本文对网络节点进行了详细的理论二分一致性和隐私保护性分析。最后，通过仿真实验验证了理论结果的有效性。
Abstract: This paper investigates the privacy-preserving bipartite consensus problem in continuous-time cooperative-competitive multi-agent systems. To prevent the leakage of initial states of network nodes while achieving bipartite consensus in networks with cooperative-competitive interactions, this paper proposes a novel privacy-preserving bipartite consensus control algorithm. This paper introduces an output mask mechanism to ensure the internal states of agents remain unobservable to other nodes. This method differs from existing privacy-preserving techniques such as differential privacy and homomorphic encryption, and this paper innovatively applies this method to cooperative-competitive multi-agent systems. Based on the proposed algorithm,a detailed theoretical analysis of bipartite consensus and privacy preservation is conducted. Finally, a numerical simulation is given to validate the effectiveness of the proposed privacy-preserving bipartite consensus algorithm.
文章引用：陈永玲. 基于输出掩码的合作竞争多智能体系统二分一致性隐私保护问题研究[J]. 理论数学, 2025, 15(4): 338-350. https://doi.org/10.12677/pm.2025.154137

参考文献

[1] Mi, W., Luo, L. and Zhong, S. (2023) Fixed-Time Consensus Tracking for Multi-Agent Systems with a Nonholomonic Dynamics. IEEE Transactions on Automatic Control, 68, 1161-1168.
https://doi.org/10.1109/tac.2022.3148312
[2] Dai, J., Yi, J. and Chai, L. (2024) Accelerating the Convergence Rate of Consensus for Second- Order Multi-Agent Systems by Memory Information. Automatica, 166, Article 111727.
https://doi.org/10.1016/j.automatica.2024.111727
[3] Zhang, W., Mao, S., Huang, J., Kocarev, L. and Tang, Y. (2021) Data-driven Resilient Con- trol for Linear Discrete-Time Multi-Agent Networks under Unconfined Cyber-Attacks. IEEE Transactions on Circuits and Systems I: Regular Papers, 68, 776-785.
https://doi.org/10.1109/tcsi.2020.3037242
[4] Tang, Z., Hill, D.J. and Liu, T. (2021) Distributed Coordinated Reactive Power Control for Voltage Regulation in Distribution Networks. IEEE Transactions on Smart Grid, 12, 312-323.
https://doi.org/10.1109/tsg.2020.3018633
[5] Jiang, Y., Liu, L. and Feng, G. (2024) Fully Distributed Adaptive Control for Output Consensus of Uncertain Discrete-Time Linear Multi-Agent Systems. Automatica, 162, Article 111531.
https://doi.org/10.1016/j.automatica.2024.111531
[6] Olfati-Saber, R. and Murray, R.M. (2004) Consensus Problems in Networks of Agents with Switching Topology and Time-Delays. IEEE Transactions on Automatic Control, 49, 1520- 1533.
https://doi.org/10.1109/tac.2004.834113
[7] Zhai, S. and Zheng, W.X. (2019) On Survival of All Agents in a Network with Cooperative and Competitive Interactions. IEEE Transactions on Automatic Control, 64, 3853-3860.
https://doi.org/10.1109/tac.2019.2892521
[8] Altafini, C. (2013) Consensus Problems on Networks with Antagonistic Interactions. IEEE Transactions on Automatic Control, 58, 935-946.
https://doi.org/10.1109/tac.2012.2224251
[9] Li, K., Ji, L., Yang, S., Li, H. and Liao, X. (2022) Couple-Group Consensus of CooperativeCompetitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method. IEEE Transactions on Cybernetics, 52, 4907-4915.
https://doi.org/10.1109/tcyb.2020.3024551
[10] Ruan, M., Gao, H. and Wang, Y. (2019) Secure and Privacy-Preserving Consensus. IEEE Transactions on Automatic Control, 64, 4035-4049.
https://doi.org/10.1109/tac.2019.2890887
[11] Shi, S., Wang, Z., Xiao, M., Jiang, G. and Cao, J. (2024) Consensus Analysis for CooperativeCompetitive Multiagent Systems under False Data Injection Attacks via Dynamic EventTriggered Observers. IEEE Transactions on Signal and Information Processing over Networks, 10, 195-204.
https://doi.org/10.1109/tsipn.2024.3375611
[12] Zhan, J., Hsieh, C.-L., Wang, I-C., Hsu, T.-S., Liau, C.-J. and Wang, D.-W. (2010) PrivacyPreserving Collaborative Recommender Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 40, 472-476.
https://doi.org/10.1109/tsmcc.2010.2040275
[13] Gao, C., Wang, Z., He, X., Liu, Y. and Yue, D. (2024) Differentially Private Consensus Control for Discrete-Time Multiagent Systems: Encoding-Decoding Schemes. IEEE Transactions on Automatic Control, 69, 5554-5561.
https://doi.org/10.1109/tac.2024.3367803
[14] Wang, J., Ke, J. and Zhang, J. (2024) Differentially Private Bipartite Consensus over Signed Networks with Time-Varying Noises. IEEE Transactions on Automatic Control, 69, 5788-5803.
https://doi.org/10.1109/tac.2024.3351869
[15] ] Wang, J. and Zhang, J. (2024) Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes. IEEE Transactions on Automatic Control, 69, 6341-6348.
https://doi.org/10.1109/tac.2024.3379387
[16] Yazdani, K., Jones, A., Leahy, K. and Hale, M. (2023) Differentially Private LQ Control. IEEE Transactions on Automatic Control, 68, 1061-1068.
https://doi.org/10.1109/tac.2022.3148710
[17] Chen, W., Liu, L. and Liu, G. (2023) Privacy-Preserving Distributed Economic Dispatch of Microgrids: A Dynamic Quantization-Based Consensus Scheme with Homomorphic Encryption. IEEE Transactions on Smart Grid, 14, 701-713.
https://doi.org/10.1109/tsg.2022.3189665
[18] Gao, H., Zhang, C., Ahmad, M. and Wang, Y. (2018) Privacy-Preserving Average Consensus on Directed Graphs Using Push-Sum. 2018 IEEE Conference on Communications and Network Security (CNS), Beijing, 30 May-1 June 2018, 1-9.
https://doi.org/10.1109/cns.2018.8433217
[19] Wang, Y. (2019) Privacy-Preserving Average Consensus via State Decomposition. IEEE Transactions on Automatic Control, 64, 4711-4716.
https://doi.org/10.1109/tac.2019.2902731
[20] Hu, J., Sun, Q., Wang, R. and Wang, Y. (2024) An Improved Privacy-Preserving Consensus Strategy for AC Microgrids Based on Output Mask Approach and Node Decomposition Mechanism. IEEE Transactions on Automation Science and Engineering, 21, 642-651.
https://doi.org/10.1109/tase.2022.3217677
[21] Liu, Y., Xie, X., Sun, J. and Yang, D. (2024) Event-Triggered Privacy Preservation Consensus Control and Containment Control for Nonlinear Mass: An Output Mask Approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 54, 4437-4447.
https://doi.org/10.1109/tsmc.2024.3379375
[22] Altafini, C. (2020) A System-Theoretic Framework for Privacy Preservation in ContinuousTime Multiagent Dynamics. Automatica, 122, Article 109253.
https://doi.org/10.1016/j.automatica.2020.109253
[23] Artstein, Z. (1977) The Limiting Equations of Nonautonomous Ordinary Differential Equations. Journal of Differential Equations, 25, 184-202.
https://doi.org/10.1016/0022-0396(77)90199-1
[24] Wang, A., He, H. and Liao, X. (2021) Event-Triggered Privacy-Preserving Average Consensus for Multiagent Networks with Time Delay: An Output Mask Approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 4520-4531.
https://doi.org/10.1109/tsmc.2019.2939680
[25] Qin, J., Zhang, G., Zheng, W.X. and Kang, Y. (2019) Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems with Actuator Faults. IEEE Transactions on Cybernetics, 49, 1605-1615.
https://doi.org/10.1109/tcyb.2018.2805167
[26] Hu, J., Sun, Q., Wang, R., Wang, B., Zhai, M. and Zhang, H. (2022) Privacy-Preserving Sliding Mode Control for Voltage Restoration of AC Microgrids Based on Output Mask Approach. IEEE Transactions on Industrial Informatics, 18, 6818-6827.
https://doi.org/10.1109/tii.2022.3141428
[27] Wang, Y., Lu, J., Zheng, W.X. and Shi, K. (2021) Privacy-Preserving Consensus for MultiAgent Systems via Node Decomposition Strategy. IEEE Transactions on Circuits and Systems I: Regular Papers, 68, 3474-3484.
https://doi.org/10.1109/tcsi.2021.3081372
[28] Manitara, N.E. and Hadjicostis, C.N. (2013) Privacy-Preserving Asymptotic Average Consensus. 2013 European Control Conference (ECC), Zurich, 17-19 July 2013, 760-765.
https://doi.org/10.23919/ecc.2013.6669251

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