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<p>Adaptive observer-based synchronization in chaotic systems with unknown slowly time-varying parameters, crucial for parameter modulation-based secure communication systems, is impeded by conventional integer-order adaptive observers’ performance limitations. To overcome this, we introduce a novel Luenberger-like observer incorporating fractional-order gradient adaptation laws. Based on the recent advances in fractional-order calculus and the Lyapunov stability theorem, these adaptation laws guarantee observation errors stability and convergence of their quadratic norm mean value. By optimizing the differentiation order, we minimize a system performance cost function, enhancing both state and unknown parameter estimation accuracy. Numerical simulations with the Chua circuit demonstrate an increase in convergence speed and an improvement in parameter estimation accuracy over the prior scheme with integer order adaptation laws. This advancement in master–slave synchronization enables the development of more robust secure communication protocols in forthcoming studies, paving the way for more reliable and efficient secure communication systems.</p>

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A Novel Secure Communication Scheme Design Using a Fractional-Order Adaptive Observer-Based Synchronization

  • 期刊论文

  • 发表日期：

    2025年2月9日

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  • Mohsen Mohamed Hadji,
  • Samir Ladaci

摘要

Adaptive observer-based synchronization in chaotic systems with unknown slowly time-varying parameters, crucial for parameter modulation-based secure communication systems, is impeded by conventional integer-order adaptive observers’ performance limitations. To overcome this, we introduce a novel Luenberger-like observer incorporating fractional-order gradient adaptation laws. Based on the recent advances in fractional-order calculus and the Lyapunov stability theorem, these adaptation laws guarantee observation errors stability and convergence of their quadratic norm mean value. By optimizing the differentiation order, we minimize a system performance cost function, enhancing both state and unknown parameter estimation accuracy. Numerical simulations with the Chua circuit demonstrate an increase in convergence speed and an improvement in parameter estimation accuracy over the prior scheme with integer order adaptation laws. This advancement in master–slave synchronization enables the development of more robust secure communication protocols in forthcoming studies, paving the way for more reliable and efficient secure communication systems.