Output Consensus for Heterogeneous Two-Time-Scale Multiagent Systems Under DoS Attacks: A Multi-Index Case

Ying Zhang; Linna Zhou; Lei Ma; Chunyu Yang; Guoqing Wang; Wei Dai

doi:10.1109/JAS.2026.125912

Volume 13 Issue 9

Sep. 2026

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(9): 2109-2118

Y. Zhang, L. Zhou, L. Ma, C. Yang, G. Wang, and W. Dai, “Output consensus for heterogeneous two-time-scale multiagent systems under DoS attacks: A multi-index case,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 9, pp. 2109–2118, Sep. 2026. doi: 10.1109/JAS.2026.125912

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Y. Zhang, L. Zhou, L. Ma, C. Yang, G. Wang, and W. Dai, “Output consensus for heterogeneous two-time-scale multiagent systems under DoS attacks: A multi-index case,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 9, pp. 2109–2118, Sep. 2026. doi: 10.1109/JAS.2026.125912

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Output Consensus for Heterogeneous Two-Time-Scale Multiagent Systems Under DoS Attacks: A Multi-Index Case

doi: 10.1109/JAS.2026.125912

Funds: This work was supported in part by the National Natural Science Foundation of China (62573418, 62203448, 62373362, 62273350, 62603682), the National Natural Science Foundation of Jiangsu Province (BK20240102), and the National Key Research and Development Program of China (2025YFE0101100)

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Author Bio:
Ying Zhang received the B.S. degree in automation from Jiangsu Normal University, in 2019, and the Ph.D. degree in control science and engineering from China University of Mining and Technology, in 2025. She was a visiting Ph.D. student with the Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada, from 2023 to 2024. She is currently a Postdoctoral Fellow with the School of Information and Control Engineering, China University of Mining and Technology. Her research interests include singularly perturbed systems, cyber-physical systems, multiagent systems, secure control, model predictive control, and reinforcement learning

Linna Zhou received the B.S. degree from the Department of Water Conservancy Engineering, North China Institute of Water Conservancy and Hydroelectric Power, in 2001 and the Ph.D. degree in control theory and control engineering from Northeastern University, in 2007. She is currently an Associate Professor with the China University of Mining and Technology. Her research interests include singularly perturbed systems, robust control, fuzzy control, and reinforcement learning

Lei Ma (Senior Member, IEEE) received the Ph.D. degree in control science and engineering from the School of Automation, Nanjing University of Science and Technology, in 2019. From 2017 to 2018, he was a visiting scholar with the Department of Computer Science, Brunel University London, U.K. He is currently an Associate Professor with the China University of Mining and Technology. His research interests include singularly perturbed systems, switched systems, networked control systems, and unmanned aerial vehicles

Chunyu Yang (Senior Member, IEEE) received the B.S. degree in applied mathematics and the Ph.D. degree in control theory and control engineering from Northeastern University, in 2002 and 2009, respectively. He was a visiting scholar at the University of Michigan, USA, from 2015 to 2016. Currently, he is a Professor with the China University of Mining and Technology. His research interests include singularly perturbed systems, industrial process operational control, cyber-physical systems, and robust control

Guoqing Wang (Member, IEEE) received the B.S. degree in electrical engineering and automation from the China University of Mining and Technology, in 2014, and the Ph.D. degree in control science and engineering from Harbin Engineering University, in 2019. From 2017 to 2019, he was a visiting scholar with the Electrical Engineering Department, Columbia University, New York, NY, USA. He is currently an Associate Professor with China University of Mining and Technology. His current research interests include robust state estimation, information fusion, and their applications in robot navigation

Wei Dai (Senior Member, IEEE) received the M.S. and Ph.D. degrees in control theory and control engineering from Northeastern University, in 2009 and 2015, respectively. From 2013 to 2015, he was a Teaching Assistant with the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. He is currently a Professor and an Outstanding Young Backbone Teacher with the China University of Mining and Technology. He was the Project Leader in several funded research projects (funds from the Natural Science Foundation of China, the Natural Science Foundation of Jiangsu Province, the Postdoctoral Science Foundation of China, and so on). His current research interests include modeling, optimization, and control of complex industrial processes, data mining, and machine learning
Corresponding author: Lei Ma, e-mail: leima@cumt.edu.cn
Received Date: 2025-06-26
Revised Date: 2025-12-12
Accepted Date: 2026-01-22

Abstract

Abstract

This article studies the output consensus issue for a class of heterogeneous two-time-scale multiagent systems (HTTSMASs) under denial-of-service (DoS) attacks. A novel output consensus control framework, integrating a resilient distributed observer and a composite controller, is built as the first attempt for HTTSMASs. By establishing a DoS attack impact interval for each communication channel, the resilient distributed observer based on asynchronous sampling is designed to resist DoS attacks. Given the inherent two-time-scale characteristics, solving the regulator equations (REs) of original HTTSMASs often leads to ill-conditioned numerical issues. To overcome this challenge, singular perturbation theory is employed to decouple the output consensus problem into a multi-index control problem for slow and fast subsystems. Specifically, a slow sub-controller is designed to achieve output tracking based on the solution of the slow subsystem’s REs, while a fast sub-controller is designed to guarantee the fast subsystem’s stability. Finally, a numerical example and an application involving a permanent magnet synchronous motor are presented to verify the effectiveness of the designed method.
- DoS attacks,
- heterogeneous multiagent systems,
- singular perturbation,
- two-time-scale

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References

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Output Consensus for Heterogeneous Two-Time-Scale Multiagent Systems Under DoS Attacks: A Multi-Index Case

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