Adaptive fuzzy fault-tolerant formation control for nonlinear multi-agent systems under cyber-physical threats

Naveed Iqbal; Fathia Moh. Al Samman; Rohma Arooj; Abdulqadir Ismail Abdullah; Mohammed M. A. Almazah; A. Y. Al-Rezami; Azmat Ullah Khan Niazi; Naveed Iqbal; Fathia Moh. Al Samman; Rohma Arooj; Abdulqadir Ismail Abdullah; Mohammed M. A. Almazah; A. Y. Al-Rezami; Azmat Ullah Khan Niazi

doi:10.3934/math.2025874

AIMS Mathematics

2025, Volume 10, Issue 8: 19586-19616. doi: 10.3934/math.2025874

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Adaptive fuzzy fault-tolerant formation control for nonlinear multi-agent systems under cyber-physical threats

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, College of Sciences, Northern Border University, Arar, Saudi Arabia
3.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
4.
Department of Computer Engineering, College of Engineering, Knowledge University, Erbil 44001, Iraq
5.
Department of Computer Engineering, Al-Kitab University, Altun Kupri, Iraq
6.
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
7.
Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

Received: 26 May 2025 Revised: 04 August 2025 Accepted: 15 August 2025 Published: 27 August 2025

This article investigated the fuzzy adaptive fault-tolerant resilient formation control issue for uncertain nonlinear multi-agent systems (MASs) with immeasurable states and under denial-of-service (DoS) attacks. Fuzzy logic systems were utilized to model unknown agents, and a fuzzy state estimator was formulated to reconstruct the agents' unknown states. A distributed resilient formation estimator was proposed to obtain the unknown leader information estimation and its high-order derivatives under DoS attacks. Based on the designed fuzzy state and resilient formation estimators, a fault-tolerant fuzzy output-feedback adaptive resilient formation control scheme was developed via the backstepping control methodology. It was proven that the developed fault-tolerant fuzzy resilient formation control scheme can guarantee that the controlled nonlinear MASs were stable and formation tracking errors converged even under unknown states, actuator faults, and DoS attacks. Finally, the proposed fuzzy adaptive fault-tolerant resilient formation control method was applied to marine surface vehicles; the simulation results and comparisons showed the effectiveness of the presented control methodology.
- multi-agent systems (MASs),
- resilient fault-tolerant control,
- fuzzy adaptive observer,
- denial-of-service (DoS) attacks,
- distributed estimation
Citation: Naveed Iqbal, Fathia Moh. Al Samman, Rohma Arooj, Abdulqadir Ismail Abdullah, Mohammed M. A. Almazah, A. Y. Al-Rezami, Azmat Ullah Khan Niazi. Adaptive fuzzy fault-tolerant formation control for nonlinear multi-agent systems under cyber-physical threats[J]. AIMS Mathematics, 2025, 10(8): 19586-19616. doi: 10.3934/math.2025874

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Abstract

This article investigated the fuzzy adaptive fault-tolerant resilient formation control issue for uncertain nonlinear multi-agent systems (MASs) with immeasurable states and under denial-of-service (DoS) attacks. Fuzzy logic systems were utilized to model unknown agents, and a fuzzy state estimator was formulated to reconstruct the agents' unknown states. A distributed resilient formation estimator was proposed to obtain the unknown leader information estimation and its high-order derivatives under DoS attacks. Based on the designed fuzzy state and resilient formation estimators, a fault-tolerant fuzzy output-feedback adaptive resilient formation control scheme was developed via the backstepping control methodology. It was proven that the developed fault-tolerant fuzzy resilient formation control scheme can guarantee that the controlled nonlinear MASs were stable and formation tracking errors converged even under unknown states, actuator faults, and DoS attacks. Finally, the proposed fuzzy adaptive fault-tolerant resilient formation control method was applied to marine surface vehicles; the simulation results and comparisons showed the effectiveness of the presented control methodology.

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