Two-layer game-based consensus security control for stochastic multiagent systems over sensor attacks

Zan Li; Kan He; Zhongjun Yang; Lian Lian; Yifei Sun; Huaici Zhao; Zan Li; Kan He; Zhongjun Yang; Lian Lian; Yifei Sun; Huaici Zhao

doi:10.3934/math.20261232

AIMS Mathematics

2026, Volume 11, Issue 9: 31185-31213. doi: 10.3934/math.20261232

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Research article

Two-layer game-based consensus security control for stochastic multiagent systems over sensor attacks

1.
College of Information Engineering, Shenyang University of Chemical Technology, Shenyang 110142, China
2.
Key Laboratory of Information Security for Petrochemical Industry in Liaoning Province, Shenyang 110142, China

Received: 15 June 2026 Revised: 01 September 2026 Accepted: 11 September 2026 Published: 23 September 2026
MSC : 93C10, 93A16, 93D50

This paper investigates distributed optimal consensus security control (CSC) for uncertain multi-agent systems (MASs) with Gaussian noise, where subsystem output channels are vulnerable to sensor attacks. A novel two-layer game framework is proposed. At the agent level, the CSC problem under Gaussian processes is modeled as a zero-sum stochastic game between the controller and the attack signal, with local optimality achieved via adaptive dynamic programming (ADP). This optimality is realized by designing a distributed control protocol, treating the attack signals as independent participants and adjusting the actions based on the consensus error. At the communication network level, the Nash equilibrium of MASs under communication constraints is derived through graphical games, ensuring global optimality. The scheme guarantees that MASs maintain optimal CSC in the sense of expectation even under severe attacks, which is validated on an islanded microgrid test system.
- Adaptive dynamic programming (ADP),
- graphical game,
- multiagent systems (MASs),
- sensor attacks,
- zero-sum game
Citation: Zan Li, Kan He, Zhongjun Yang, Lian Lian, Yifei Sun, Huaici Zhao. Two-layer game-based consensus security control for stochastic multiagent systems over sensor attacks[J]. AIMS Mathematics, 2026, 11(9): 31185-31213. doi: 10.3934/math.20261232

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Abstract

This paper investigates distributed optimal consensus security control (CSC) for uncertain multi-agent systems (MASs) with Gaussian noise, where subsystem output channels are vulnerable to sensor attacks. A novel two-layer game framework is proposed. At the agent level, the CSC problem under Gaussian processes is modeled as a zero-sum stochastic game between the controller and the attack signal, with local optimality achieved via adaptive dynamic programming (ADP). This optimality is realized by designing a distributed control protocol, treating the attack signals as independent participants and adjusting the actions based on the consensus error. At the communication network level, the Nash equilibrium of MASs under communication constraints is derived through graphical games, ensuring global optimality. The scheme guarantees that MASs maintain optimal CSC in the sense of expectation even under severe attacks, which is validated on an islanded microgrid test system.

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