Study on P-type ILC for Hilfer-type fractional-order quaternion-valued systems with initial state deviation with application in soft robotic actuators | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 2, 2025, Pages 1-22 PDF (618.62 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.405773.1183 | ||
| Authors | ||
| S Sunmitha1; D Vivek1; Rabha Ibrahim* 2 | ||
| 1PSG College of Arts | ||
| 2ieee | ||
| Abstract | ||
| This paper examines a P-type iterative learning control law for linear quaternion-valueddifferential equations with respected to Hilfer fractional order (arbitrary fractional order power). Convergence analysis is studied for both open-loop and closed-loop schemes, incorporating initial state deviations and random disturbances within the -norm concept. This study employs the properties of Mitta-Leer functions to derive theoretical results, which are further validated through numerical examples that showcase the e ectiveness of the proposed approach, with application in soft robotic actuators. The results highlight the potential of Hilfer-type fractional-order iterative learning techniques in improving the performance of control systems, particularly in scenarios with uncertainties and disturbances. Future work could extend the proposed ideas to nonlinear switched quaternion-valued systems, study adaptive learning strategies, and investigate the impact of HFD on system performance. Additionally, incorporating real-world applications such as robotics, signal processing, and control engineering could further validate the practical signi cance of this study. | ||
| Keywords | ||
| Hilfer fractional derivative; Iterative learning control; Quaternion systems; Convergence; Mittag-Leer function | ||
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