Mamdani fuzzy parameter estimation of fractional-order large-scale interconnected systems

Mourad Elloumi; Omar Naifar; Abdulaziz J Alateeq; Mansoor Alturki; Khalid Alqunun; Tawfik Guesmi; Mourad Elloumi; Omar Naifar; Abdulaziz J Alateeq; Mansoor Alturki; Khalid Alqunun; Tawfik Guesmi

doi:10.3934/math.2025996

AIMS Mathematics

2025, Volume 10, Issue 9: 22382-22405. doi: 10.3934/math.2025996

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Mamdani fuzzy parameter estimation of fractional-order large-scale interconnected systems

1.
Faculty of Sciences of Gafsa, University of Gafsa, Gafsa, Tunisia
2.
Laboratory of Sciences and Technology of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, P.O. Box 1173, Sfax 3038, Tunisia
3.
Higher Institute of Applied Science and Technology of Kairouan, University of Kairouan, Kairouan, Tunisia
4.
Control and Energy Management Laboratory, National School of Engineering, Sfax University, Sfax, Tunisia
5.
Department of Electrical Engineering, College of Engineering, University of Ha'il, Ha'il 2240, Saudi Arabia

Received: 06 August 2025 Revised: 13 September 2025 Accepted: 21 September 2025 Published: 28 September 2025
MSC : 26A33, 93B30, 93E11, 93C42, 93C10, 93D20, 60G22, 65L09

This work presents a generalization and a comparative study of the recursive maximum likelihood estimation algorithm for large-scale interconnected nonlinear systems, extending existing integer-order frameworks to fractional-order dynamics. While prior research introduced Mamdani fuzzy-based parameter estimators for networked integer-order interconnected nonlinear autoregressive moving average with exogenous input (INARMAX) models, this study addresses the challenges of time-varying fractional-order systems with memory-dependent behavior and stochastic disturbances. A novel recursive estimator is developed by integrating the Grünwald–Letnikov fractional difference operator into the prediction error framework, coupled with a Mamdani fuzzy supervisor to dynamically tune the forgetting factors. The proposed method is rigorously validated through simulations on interconnected subsystems with time-varying coefficients and nonlinear couplings. The results demonstrate a 30%–50% reduction in steady-state prediction errors and 40%–60% faster convergence compared with integer-order benchmarks, alongside superior robustness to noise ($\sigma_i^2 \leq 0.25$) and abrupt parameter changes. This work establishes the first fuzzy-augmented fractional Maximum Likelihood Estimation (MLE) framework for large-scale systems, offering theoretical guarantees and empirical validation. Applications in power networks, biomedical systems, and industrial processes with hereditary dynamics are highlighted. The study underscores the necessity of fractional-order modeling in complex systems and provides a scalable solution for real-world deployment.
- large-scale systems,
- fractional calculus,
- parameter estimation,
- Mamdani fuzzy logic,
- recursive maximum likelihood,
- comparative analysis
Citation: Mourad Elloumi, Omar Naifar, Abdulaziz J Alateeq, Mansoor Alturki, Khalid Alqunun, Tawfik Guesmi. Mamdani fuzzy parameter estimation of fractional-order large-scale interconnected systems[J]. AIMS Mathematics, 2025, 10(9): 22382-22405. doi: 10.3934/math.2025996

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Abstract

This work presents a generalization and a comparative study of the recursive maximum likelihood estimation algorithm for large-scale interconnected nonlinear systems, extending existing integer-order frameworks to fractional-order dynamics. While prior research introduced Mamdani fuzzy-based parameter estimators for networked integer-order interconnected nonlinear autoregressive moving average with exogenous input (INARMAX) models, this study addresses the challenges of time-varying fractional-order systems with memory-dependent behavior and stochastic disturbances. A novel recursive estimator is developed by integrating the Grünwald–Letnikov fractional difference operator into the prediction error framework, coupled with a Mamdani fuzzy supervisor to dynamically tune the forgetting factors. The proposed method is rigorously validated through simulations on interconnected subsystems with time-varying coefficients and nonlinear couplings. The results demonstrate a 30%–50% reduction in steady-state prediction errors and 40%–60% faster convergence compared with integer-order benchmarks, alongside superior robustness to noise ($\sigma_i^2 \leq 0.25$) and abrupt parameter changes. This work establishes the first fuzzy-augmented fractional Maximum Likelihood Estimation (MLE) framework for large-scale systems, offering theoretical guarantees and empirical validation. Applications in power networks, biomedical systems, and industrial processes with hereditary dynamics are highlighted. The study underscores the necessity of fractional-order modeling in complex systems and provides a scalable solution for real-world deployment.

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