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RESEARCH ARTICLE

Adaptive neural fault-tolerant consensus control of discrete-time fractional-order multi-agent systems for smart energy networks

Naveed Iqbal1 ,  Abid Raza2 ,  Azmat Ullah Khan Niazi2,* ,  Rashed Abu Hammour3 ,  Shamas ur Rehman4
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1 Department of Mathematics, College of Science, University of Ha’il, Ha’il , Saudi Arabia
2 Department of Mathematics and Statistics, The University of Lahore, Sargodha , Pakistan
3 Faculty of Technical Education, Hourani Center for Applied Scientific Research (HCASR), Al-Ahliyya Amman University, Amman , Jordan
4 Department of Mathematics, Mai Nefhi college of Science, Asmara , Eritrea
IJOCTA, 026330216 https://doi.org/10.36922/IJOCTA026330216
Received: 16 August 2026 | Revised: 12 September 2026 | Accepted: 18 September 2026 | Published online: 27 October 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper investigates leader-following consensus for discrete-time fractional-order multi-agent systems with unknown nonlinear dynamics, bounded disturbances, and actuator faults arising in distributed smart energy applications. An adaptive neural-assisted fault-tolerant controller is developed by combining a Caputo-type fractional-order sliding variable with an online Radial Basis Function Neural Network (RBFNN). The RBFNN approximates the unknown nonlinear dynamics, while an adaptive weight-update law compensates {for} the neural approximation error. Actuator degradation is represented through a bounded loss-of-effectiveness factor and additive fault bias, allowing the controller to accommodate different actuator-fault conditions without requiring their exact profiles. A discrete fractional{-order} Lyapunov analysis is established to derive sufficient conditions ensuring {the} boundedness of the sliding variable, {the} neural-weight estimation error and {the} closed-loop signals. The consensus dynamics are subsequently characterized through the stable fractional{-order} error system driven by the vanishing sliding variable. Numerical simulations involving actuator degradation, external disturbances, parameter sensitivity, network scalability{,} and comparative benchmarks demonstrate the effectiveness of the proposed method in reducing consensus error and maintaining coordinated leader-following behavior under uncertain operating conditions.

Graphical abstract
Keywords
Discrete time fractional-order
multi-agent systems
Leader-follower consensus
Fault-tolerant control
Radial Basis Function Neural
Network (RBFNN)
Adaptive neural approximation
Sliding mode control
Smart energy systems
Funding
None.
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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