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<p>In this study, we investigate Ulam stability principles for initial value problems involving impulsive fractional differential equations, specifically those defined using the Hilfer fractional derivative (HFD). We establish the existence of solutions for such equations and extend our analysis to the context of iterative learning control (ILC). Subsequently, we examine how varying an iterative state, which initially differs from the given starting condition, impacts the system’s behavior. Furthermore, we propose a proportional type iterative learning principle that incorporates the original learning conditions, ensuring that each output eventually converges to the desired trajectory within a finite time period. We also present a convergence result to support the effectiveness of the approach. To demonstrate the validity of our theoretical findings, we provide a numerical example that illustrates the results for various iteration steps.</p>

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Studies on convergence and stability of iterative learning control in impulsive fractional systems with Hilfer fractional derivative

  • 期刊论文

  • 发表日期：

    2025年12月16日

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  • D. Vivek,
  • S. Sunmitha,
  • E. M. Elsayed

摘要

In this study, we investigate Ulam stability principles for initial value problems involving impulsive fractional differential equations, specifically those defined using the Hilfer fractional derivative (HFD). We establish the existence of solutions for such equations and extend our analysis to the context of iterative learning control (ILC). Subsequently, we examine how varying an iterative state, which initially differs from the given starting condition, impacts the system’s behavior. Furthermore, we propose a proportional type iterative learning principle that incorporates the original learning conditions, ensuring that each output eventually converges to the desired trajectory within a finite time period. We also present a convergence result to support the effectiveness of the approach. To demonstrate the validity of our theoretical findings, we provide a numerical example that illustrates the results for various iteration steps.