Theory, Modeling and Applications of Fractional-Order Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: closed (15 September 2024) | Viewed by 2930

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Department of Electrical Engineering, Section of Mechatronics, Center of Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), México City, Mexico
Interests: analysis and design of controllers for nonlinear systems and applications; control of servomechanisms; computer-controlled systems; robot control; unmanned aerial and ground autonomous vehicle control
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Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Av. Santa Isabel 1186, Santiago 8330601, Chile
Interests: robust adaptive control (linear and nonlinear, fractional and integer order); system identification and parameter estimation; intelligent control and applications; technology for automation; applied control to mining, energy, electric power systems, electro-medicine and wine industries
Special Issues, Collections and Topics in MDPI journals

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Dear Colleagues:

Mathematics runs Special Issues to create collections of papers on specific topics. The aim is to establish a community of authors and readers to discuss the latest research and develop new ideas and research directions. Special Issues are led by Guest Editors who are experts in the subject and oversee the editorial process for papers. Papers published in a Special Issue will be collected together on a dedicated page of the journal’s website. For any inquiries related to a Special Issue, please contact the Editorial Office.

This Special Issue is devoted to the “Theory, Modeling and Applications of Fractional-Order Systems”. Although the concept of fractional-order integrals and derivatives can be traced back to the letter from Leibniz to L’Hôpital written in 1695, it was only in the late seventies that fractional-order operators were introduced in the scientific community, and it is today understood as the study of integrals and derivatives whose order is not composed of integers but real numbers. In the last 20 years these concepts have been profusely studied and applied in a wide area of physical and mathematical problems.

Prof. Dr. Rafael Castro-Linares
Prof. Dr. Manuel A. Duarte-Mermoud
Guest Editors

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Keywords

  • fractional-order systems
  • fractional-order control
  • fractional-order identification
  • fractional-order calculus
  • fractional-order operators
  • fractional-order estimation

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Published Papers (2 papers)

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Research

23 pages, 1677 KiB  
Article
Design and Comparison of Fractional-Order Controllers in Flotation Cell Banks and Flotation Columns Used in Copper Extraction Processes
by Manuel A. Duarte-Mermoud, Abdiel Ricaldi-Morales, Juan Carlos Travieso-Torres and Rafael Castro-Linares
Mathematics 2024, 12(17), 2789; https://doi.org/10.3390/math12172789 - 9 Sep 2024
Viewed by 1017
Abstract
This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for [...] Read more.
This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area. Full article
(This article belongs to the Special Issue Theory, Modeling and Applications of Fractional-Order Systems)
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22 pages, 1528 KiB  
Article
Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays
by Yihong Liu and Yeguo Sun
Mathematics 2024, 12(7), 1108; https://doi.org/10.3390/math12071108 - 7 Apr 2024
Cited by 1 | Viewed by 1133
Abstract
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the [...] Read more.
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems. Full article
(This article belongs to the Special Issue Theory, Modeling and Applications of Fractional-Order Systems)
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