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<p>The current study presents a novel computational approach utilizing Krawtchouk wavelets (KWs) to solve fractional optimal control problems (FOCPs). The proposed method leverages the fractional-order Riemann–Liouville integral and an operational matrix of integration, specifically tailored for KWs, to transform FOCPs into a system of algebraic equations. By utilizing the Legendre–Gauss quadrature rule, the original problem is approximated in terms of unknown coefficients, significantly simplifying its complexity. The necessary conditions for optimization are solved iteratively using Newton’s method, ensuring accuracy and efficiency. A comprehensive convergence analysis confirms the reliability of the approach, while numerical examples demonstrate its superior performance compared to existing wavelet-based methods. The proposed method effectively captures the memory and hereditary characteristics inherent in fractional systems, making it a powerful tool for addressing real-world fractional optimal control models across various applications.</p>

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A novel projection method utilizing Krawtchouk wavelets for solving fractional-order optimal control models

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Hajar Mohammadi,
  • Habibollah Saeedi,
  • Mohammad Izadi

摘要

The current study presents a novel computational approach utilizing Krawtchouk wavelets (KWs) to solve fractional optimal control problems (FOCPs). The proposed method leverages the fractional-order Riemann–Liouville integral and an operational matrix of integration, specifically tailored for KWs, to transform FOCPs into a system of algebraic equations. By utilizing the Legendre–Gauss quadrature rule, the original problem is approximated in terms of unknown coefficients, significantly simplifying its complexity. The necessary conditions for optimization are solved iteratively using Newton’s method, ensuring accuracy and efficiency. A comprehensive convergence analysis confirms the reliability of the approach, while numerical examples demonstrate its superior performance compared to existing wavelet-based methods. The proposed method effectively captures the memory and hereditary characteristics inherent in fractional systems, making it a powerful tool for addressing real-world fractional optimal control models across various applications.