Robust Bipartite Containment Control of Multi-Agent Systems under Stochastic Disturbances and False Data Injection Attacks via Zero-Sum Game Strategy

Articles in Press

Document Type : Research Paper

Authors
Ammar Alsinai 1
Ibraheem Al-Hejri 1
Azmat Ullah Khan Niazi 2
Maryam Iqbal 2
Aseel Smerat 3 , 4
1 Department of Computer Science, College of Engineering and Information Technology, Onaizah Colleges, Qassim 56447, Saudi Arabia
2 Department of Mathematics and Statistics, University of Lahore, Sargodha, Pakistan
3 Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India
4 Faculty of Educational Sciences, AI-Ahliyya Amman University, Amman 19328, Jordan
10.22055/jacm.2025.48738.5461
Abstract
This paper addresses the problem of bipartite containment control for multi-agent systems (MASs) subjected to simultaneous stochastic disturbances and false data injection attacks (FDIA). The interactions among agents are modeled by signed directed graphs, which represent both cooperative and antagonistic relationships. A novel hybrid disturbance model is introduced to capture the challenges posed by both stochastic and adversarial inputs, reflecting the complexities of uncertainties in dynamic environments. Furthermore, the agents' communication channels are assumed to be vulnerable to FDIAs, which corrupt neighbor information and further complicate the containment objective. To tackle these issues, a zero-sum differential graphical game framework is proposed, leading to a robust control strategy that ensures system stability and containment performance even under hybrid disturbances. The theoretical convergence of the proposed method is rigorously demonstrated, and simulation results confirm its effectiveness and robustness. Practical application scenarios, such as Autonomous Vehicle Platooning under Adversarial and Noisy Conditions and Drone Swarm Surveillance under GPS Spoofing and Sensor Noise, illustrate the importance of maintaining coordinated behavior in the presence of real-world uncertainties.
Keywords
Bipartite Containment Control
Multi-Agent Systems (MASs)
False Data Injection Attacks (FDIA)
Robust Distributed Control
Cyber-Physical Security
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Gao, Z., Zhao, N., Zong, G., Zhao, X., Secure consensus control for constrained multi-agent systems against intermittent denial-of-service attacks: an adaptive dynamic programming method, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 14(4), 2024, 705–716.
[2] Diaz-Garcia, G., Guatibonza, D., Giraldo, L. F., Distributed reconfiguration for resilient synchronization of multi-agent systems, IEEE Access, 9, 2021, 140235–140247.
[3] Tang, D., Pang, N., Wang, X., Reinforcement learning-based event-triggered constrained containment control for perturbed multiagent systems, IEEE Transactions on Signal and Information Processing over Networks, 10, 2024, 820–832.
[4] Yu, X., Wang, G., Jia, L., Zhang, H., Event-triggered practical fixed-time containment control for stochastic multiagent systems with input delay, IEEE Transactions on Fuzzy Systems, 32(5), 2024, 2762–2774.
[5] Chen, W., Wang, Z., Dong, H., Mao, J., Liu, G. P., Privacy-preserving distributed economic dispatch of microgrids over directed networks via state decomposition: A fast consensus algorithm, IEEE Transactions on Industrial Informatics, 20(3), 2023, 4092–4102.
[6] Liu, D., Mao, Z., Jiang, B., Xu, L., Simplified ADP-based distributed event-triggered fault-tolerant control of heterogeneous nonlinear multiagent systems with full-state constraints, IEEE Transactions on Circuits and Systems I: Regular Papers, 71(8), 2024, 3820–3832.
[7] Maaruf, M., El Ferik, S., Actor–critic learning-based finite-time secure formation maneuver control of multiagent systems with deception attacks and backlash-like hysteresis, SSRN, 5145107.
[8] Abate, A., et al., Index Transactions on Automatic Control Vol. 66, IEEE Transactions on Automatic Control, 66(12), 2021.
[9] Chen, B., Lin, B., Li, M., Li, Z., Zhang, X., Shi, M., Qin, K., Event-triggered-based neuroadaptive bipartite containment tracking for networked unmanned aerial vehicles, Drones, 9(4), 2025, 317.
[10] Liu, Z., Zhang, H., Wang, Z., Bipartite containment control of multi-agent systems under DoS attacks: an event-triggered scheme, International Journal of Robust and Nonlinear Control, 35(2), 2025, 479–495.
[11] Cheng, J., Wu, J., Zhan, X., Han, T., Wu, B., Adaptive bipartite output containment control of heterogeneous multi-agent systems against FDI attacks, Asian Journal of Control, 26(6), 2024, 2991–3001.
[12] Sekercioglu, P., Panteley, E., Sarras, I., Loría, A., Marzat, J., Distributed bipartite containment tracking over signed networks with multiple leaders, IEEE Transactions on Control of Network Systems, 11(4), 2024, 1975–1985.
[13] Yang, Y., Shi, P., Wang, S., Chambers, J., Bipartite containment of heterogeneous multi-agent systems under denial-of-service attacks: a historical information-based control scheme, International Journal of Robust and Nonlinear Control, 34(5), 2024, 3126–3141.
[14] Zhang, L., Liu, S., Hua, C., Dynamic event/self-triggered full-state bipartite containment control for nonlinear multi-agent systems under switching topologies, IEEE Transactions on Circuits and Systems I: Regular Papers, 71(4), 2024, 1852–1862.
[15] Zhang, Y., Sun, J., Li, H., He, W., Event-triggered adaptive bipartite containment control for stochastic multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(9), 2021, 5843–5852.
[16] Guo, X., Ma, H., Liang, H., Zhang, H., Command-filter-based fixed-time bipartite containment control for a class of stochastic multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(6), 2021, 3519–3529.
[17] Zhang, L., Liu, S., Hua, C., Distributed bipartite containment control of high-order nonlinear multi-agent systems with time-varying powers, IEEE Transactions on Circuits and Systems I: Regular Papers, 70(3), 2022, 1371–1380.
[18] Li, C., Xia, H., Zhu, H., Asynchronous bipartite containment control of second-order multi-agent systems under switching topologies, Transactions of the Institute of Measurement and Control, 45(3), 2023, 492–501.
[19] Zhang, H., Zhou, Y., Liu, Y., Sun, J., Cooperative bipartite containment control for multi-agent systems based on an adaptive distributed observer, IEEE Transactions on Cybernetics, 52(6), 2020, 5432–5440.
[20] Zhao, Y., Zhu, F., Bipartite containment control of nonlinear multi-agent systems with unknown inputs and state constraints, International Journal of Adaptive Control and Signal Processing, 38(5), 2024, 1854–1877.
[21] Liu, Y., Zhang, H., Shi, Z., Gao, Z., Neural-network-based finite-time bipartite containment control for fractional-order multi-agent systems, IEEE Transactions on Neural Networks and Learning Systems, 34(10), 2022, 7418–7429.
[22] Zhang, J., Zhang, H., Li, W., Wang, Y., Adaptive event-triggered bipartite containment control of linear multiagent systems under directed topologies, IEEE Transactions on Control of Network Systems, 10(1), 2022, 516–525.
[23] Shi, L., Li, W., Shi, M., Lin, B., Event-based bipartite containment control for multi-agent networks subject to communication delay, IEEE Transactions on Network Science and Engineering, 11(2), 2023, 2024–2033.
[24] Gu, X., Zhou, W., Wu, Y., Wu, W., Yang, G., Bipartite containment control for multi-agent systems under fixed and Markov switching topologies, International Journal of Control, Automation and Systems, 21(4), 2023, 1331–1337.
[25] Zhu, Z. H., Hu, B., Guan, Z. H., Zhang, D. X., Li, T., Observer-based bipartite containment control for singular multi-agent systems over signed digraphs, IEEE Transactions on Circuits and Systems I: Regular Papers, 68(1), 2020, 444–457.
[26] Liu, Z., Zhan, X., Wu, J., Yan, H., Bipartite fixed-time output containment control of heterogeneous linear multi-agent systems, AIMS Mathematics, 8(3), 2023, 7419–7436.
[27] Wu, X., Bipartite containment control for delayed multiagent systems with Markovian switching topologies under impulsive attacks, IEEE Access, 11, 2023, 37324–37334.
[28] Wang, L., Wu, J., Zhan, X. S., Han, T., Yan, H., Fixed-time bipartite containment of multi-agent systems subject to disturbance, IEEE Access, 8, 2020, 77679–77688.
[29] Hou, Y., Yan, Y., Yu, S., Observer-based bipartite containment control of multi-agent systems with input and output quantization, 14th International Conference on Information Science and Technology (ICIST), IEEE, December 2024, 281–286.
[30] Li, Z., Wu, J., Zhan, X., Han, T., Yan, H., Distributed finite-time adaptive containment and bipartite containment control for nonlinear multi-agent systems, International Journal of Control, Automation and Systems, 21(5), 2023, 1570–1580.
[31] Yao, Y., Yuan, J., Chen, T., Yang, X., Yang, H., Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints, Mathematical Biosciences and Engineering, 20, 2023, 17296–17323.
[32] Thummalapeta, M., Liu, Y. C., Survey of containment control in multi-agent systems: concepts, communication, dynamics, and controller design, International Journal of Systems Science, 54(14), 2023, 2809–2835.
[33] Zou, W., Huang, Y., Ahn, C. K., Xiang, Z., Containment control of linear multi-agent systems with stochastic disturbances via event-triggered strategies, IEEE Systems Journal, 14(4), 2020, 4810–4819.
[34] Cai, Y., Zhang, H., Wang, Y., Gao, Z., He, Q., Adaptive bipartite fixed-time, time-varying output formation-containment tracking of heterogeneous linear multiagent systems, IEEE Transactions on Neural Networks and Learning Systems, 33(9), 2021, 4688–4698.
[35] Yan, L., Liu, J., Chen, C. P., Zhang, Y., Wu, Z., Liu, Z., Game-based adaptive fuzzy optimal bipartite containment of nonlinear multiagent systems, IEEE Transactions on Fuzzy Systems, 32(3), 2023, 1455–1465.
[36] Cheng, J., Zhan, X., Wu, J., Yan, H., Adaptive bipartite output containment control of heterogeneous multi-agent systems based on the output regulation approach, International Journal of Control, Automation and Systems, 22(1), 2024, 186–195.
[37] Wu, Y., Ma, H., Chen, M., Li, H., Observer-based fixed-time adaptive fuzzy bipartite containment control for multiagent systems with unknown hysteresis, IEEE Transactions on Fuzzy Systems, 30(5), 2021, 1302–1312.
[38] Khan, A., Niazi, A. U. K., Rehman, S., Ahmed, S., Hostile-based bipartite containment control of nonlinear fractional multi-agent systems with input delays: a signed graph approach under disturbance and switching networks, AIMS Mathematics, 9(5), 2024, 12678–12699.
[39] Song, Y., Zhao, L., Fast finite-time adaptive backstepping containment control for high-order stochastic nonlinear multi-agent systems, International Journal of Adaptive Control and Signal Processing, 38(3), 2024, 1039–1060.
[40] Zhang, T., Li, H., Liu, J., Lu, D., Xie, S., Luo, J., Distributed multiple-bipartite consensus in networked Lagrangian systems with cooperative–competitive interactions, Nonlinear Dynamics, 106(3), 2021, 2229–2244.
[41] Javier Benavides, D., Arévalo-Cordero, P., Gonzalez, L. G., Hernández-Callejo, L., Jurado, F., Aguado, J. A., Method of monitoring and detection of failures in PV system based on machine learning techniques, Revista Facultad de Ingeniería Universidad de Antioquia, 102, 2022, 26-43.
Journal of Applied and Computational Mechanics

Articles in Press, Corrected Proof
Available Online from 23 November 2025