An Efficient and Robust Numerical Solver for Impulsive Control of Fractional Chaotic Systems

Moniri, Zahra; Moghaddam, Behrouz Parsa; Roudbaraki, Morteza Zamani

doi:10.1155/2023/9077924

Cited by 6 publications

(5 citation statements)

References 49 publications

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“…Based on Tables 3 and 4, all results are improved compared to the finite difference [34] and IQS [37] algorithms, respectively. Furthermore, the results are also studied in Figures 3a and 4a for ∆ = 1 32 and various values of ϱ * (t) = r + 0.01 cos t…”

Section: B-spline Algorithmmentioning

confidence: 99%

“…In recent years, the field of fractional calculus has garnered substantial interest among researchers, owing to its extensive applications in various scientific and engineering domains. This mathematical discipline proves invaluable in refining models employed in fluid mechanics, viscoelasticity, chemistry, physics, finance, and other scientific disciplines [1][2][3][4]. This surge in research activity underscores the dynamic nature of fractional calculus, reflecting its continual evolution and the ongoing quest to enhance mathematical models crucial for addressing real-world challenges.…”

Section: Introductionmentioning

confidence: 99%

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Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators

Tanha,

Parsa Moghaddam,

Ilie

2024

Computation

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This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm’s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature.

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Section: B-spline Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators

Tanha,

Parsa Moghaddam,

Ilie

2024

Computation

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“…1 The existence and uniqueness problems of FDEs with constant delay and the stability of their solutions are crucial topics in the field of fractional differential equations. Many renowned scientists, such as Ahmed et al, 2 Moniri et al, 3 Vivek et al, 4 Mahmudov et al, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Khusainov et al, 23 Podlubny, 24 and Sousa et al 1,25 have made significant contributions to these problems. 1,[26][27][28][29][30][31][32] In conclusion, fractional differential equations and pseudo-analysis are fascinating areas of research with wide-ranging applications in various fields.…”

Section: Article Pubsaiporg/aip/jmpmentioning

confidence: 99%

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Asadzade,

Mahmudov

2024

Journal of Mathematical Physics

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In this write-up, we focus on pseudo-Hilfer-type fractional order delayed differential equations with bounded definite integral initial conditions on the time interval [0, T]. We begin by establishing relevant lemmas. Then, we derive the solution to the homogeneous Hilfer-type pseudo-fractional order retarded differential equation that satisfies the appropriate initial condition using classical methods. Next, we obtain explicit formulas for solutions to linear inhomogeneous Hilfer-type pseudo-fractional time retarded differential equations with constant coefficients, employing classical ideas. Furthermore, we investigate the existence and uniqueness of the solution of the Hilfer-type pseudo-fractional order delayed differential equation and demonstrate the stability of the given differential equation in the Ulam-Hyers sense on the time interval [0, T].

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“…This is because the conventional physical-based model may take some time to converge during tuning when running with the optimization tool. To increase the convergence's speed while maintaining the system's accuracy, the knee model is best represented in discrete form or numerical computation [60]. Therefore, the conversion of the physical-based model into a numerical computation model was done to increase convergence speed during the fine-tuning process using PSO.…”

Section: Nonlinear Knee Extension Model Developmentmentioning

confidence: 99%

Adaptive Sliding Mode Feedback Control Algorithm for a Nonlinear Knee Extension Model

et al. 2023

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Functional electrical stimulation (FES) has been widely used to treat spinal cord injury (SCI) patients. Many research studies employ a closed-loop FES system to monitor the stimulated muscle response and provide a precise amount of charge to the muscle. However, most closed-loop FES devices perform poorly and sometimes fail when muscle nonlinearity effects such as fatigue, time delay response, stiffness, spasticity, and subject change happen. The poor performance of the closed-loop FES device is mainly due to discrepancies in the feedback control algorithms. Most of the existing feedback control algorithms were not designed to adapt to new changes in patients with different nonlinearity effects, resulting in early muscle fatigue. Therefore, this research proposes an adaptive sliding mode (SM) feedback control algorithm that could adapt and fine-tune internal control settings in real-time according to the current subject’s nonlinear and time-varying muscle response during the rehabilitation (knee extension) exercise. The adaptive SM feedback controller consists mainly of system identification, direct torque control, and tunable feedback control settings. Employing the system identification unit in the feedback control algorithm enables real-time self-tuning and adjusting of the SM internal control settings according to the current patient’s condition. Initially, the patient’s knee trajectory response was identified by extracting meaningful information, which included time delay, rise time, overshoot, and steady-state error. The extracted information was used to fine-tune and update the internal SM control settings. Finally, the performance of the proposed adaptive SM feedback control algorithm in terms of system response time, stability, and rehabilitation time was analysed using a nonlinear knee model. The findings from the simulation results indicate that the adaptive SM feedback controller demonstrated the best control performance in accurately tracking the desired knee angle movement by having faster response times, smaller overshoots, and lower steady-state errors when compared with the conventional SM across four reference angle settings (20°, 30°, 40°, and 76°). The adaptive feedback SM controller was also observed to compensate for muscle nonlinearities, including fatigue, stiffness, spasticity, time delay, and other disturbances.

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An Efficient and Robust Numerical Solver for Impulsive Control of Fractional Chaotic Systems

Cited by 6 publications

References 49 publications

Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators

Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Adaptive Sliding Mode Feedback Control Algorithm for a Nonlinear Knee Extension Model

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