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

• Published in: International journal of dynamics and control Vol. 13; no. 9
• Main Authors: Mohammadi, Hajar, Saeedi, Habibollah, Izadi, Mohammad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025; Springer Nature B.V
• Subjects: Complexity; Control; Control and Systems Theory; Dynamical Systems; Engineering; Optimal control; Optimization; Quadratures; Vibration; Wavelet analysis; 35N70; Liouville-Caputo operator; Krawtchouk wavelet; Optimal control; 41A10; Convergent analysis; 65L20; Primary 65L60
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-025-01796-2

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.