Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control

Majid Roohi, Chongqi Zhang*, Mostafa Taheri, Andreas Basse-O’Connor

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems.

Original languageEnglish
Article number682
JournalFractal and Fractional
Number of pages19
Publication statusPublished - Sept 2023


  • adaptive SMC
  • delayed neural networks
  • fractional-order delayed systems
  • Lyapunov stability theorem
  • synchronization


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