Finite-time formation control with prescribed performance for multi-agent systems against FDI attacks using neural network observers

Naveed Iqbal; Meraa Arab; Saba Shaheen; Salma Trabelsi; Naveed Iqbal; Meraa Arab; Saba Shaheen; Salma Trabelsi

doi:10.3934/math.2026273

AIMS Mathematics

2026, Volume 11, Issue 3: 6592-6621. doi: 10.3934/math.2026273

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Research article

Finite-time formation control with prescribed performance for multi-agent systems against FDI attacks using neural network observers

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan

Received: 04 January 2026 Revised: 17 February 2026 Accepted: 04 March 2026 Published: 16 March 2026
MSC : 26A33, 34k37

The research developed a resilient time-varying formation control strategy with prescribed-time convergence to a bounded residual set for non-strict-feedback second-order MASs to maintain accurate tracking under these conditions. Neural networks function to predict unknown nonlinear dynamics, while a state observer based on neural networks uses partial leader information to reconstruct unmeasured states. The effects of FDI attacks and communication uncertainties were addressed through matrix equalities/inequalities that solve Laplacian asymmetry problems. The proposed method achieves semi-global practical finite-time stability because it maintains all closed-loop signals within their bounded limits while tracking errors stay within their defined performance limits. The simulation results showed that formation errors achieve the prescribed bounds in finite time while maintaining stability and reliable coordination under adversarial and uncertain conditions, which demonstrates the method's robustness and scalability.
- finite-time control,
- multi-agent systems,
- FDI attack,
- Lyapunov function,
- time-varying formation control,
- prescribed performance control,
- neural network
Citation: Naveed Iqbal, Meraa Arab, Saba Shaheen, Salma Trabelsi. Finite-time formation control with prescribed performance for multi-agent systems against FDI attacks using neural network observers[J]. AIMS Mathematics, 2026, 11(3): 6592-6621. doi: 10.3934/math.2026273

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Abstract

The research developed a resilient time-varying formation control strategy with prescribed-time convergence to a bounded residual set for non-strict-feedback second-order MASs to maintain accurate tracking under these conditions. Neural networks function to predict unknown nonlinear dynamics, while a state observer based on neural networks uses partial leader information to reconstruct unmeasured states. The effects of FDI attacks and communication uncertainties were addressed through matrix equalities/inequalities that solve Laplacian asymmetry problems. The proposed method achieves semi-global practical finite-time stability because it maintains all closed-loop signals within their bounded limits while tracking errors stay within their defined performance limits. The simulation results showed that formation errors achieve the prescribed bounds in finite time while maintaining stability and reliable coordination under adversarial and uncertain conditions, which demonstrates the method's robustness and scalability.

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