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Fractal Fract
Special Issues
New Developments in Tracking and Stabilization of Fractional-Order Systems
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New Developments in Tracking and Stabilization of Fractional-Order Systems

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 15 September 2025 | Viewed by 3057

Special Issue Editors

Dr. Sakthivel Ramalingam

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Vellore Institute of Technology, Chennai 600127, Tamil Nadu, India
Interests: stability and stabilization; fractional-order systems; complex dynamical systems
Dr. Parivallal Arumugam

E-Mail Website
Guest Editor
Department of Mathematics, SRM Institute of Science and Technology, Chennai 603203, Tamil Nadu, India
Interests: robust control; stabilization; fractional-order systems; multi-agent systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The concept of fractional calculus extends the derivatives and integrals to non-integer orders in a generalized manner. Systems that incorporate fractional integrals and derivatives in their dynamical models are known as fractional order systems. Various definitions exist for the fractional derivative, including the Riemann-Liouville, Caputo, and so on, each displaying unique characteristics. Alongside fractional derivatives, fractional-order systems also involve fractional integrals. The study of fractional-order systems has garnered significant attention due to their ability to provide more accurate descriptions of many real-world systems. The applications of fractional-order systems can be found in several areas such as signal processing, biomedical systems, signal processing, and so on. Fractional-order systems and control have become an area of active research and attention due to their potential to provide more accurate modeling and control solutions for various complex processes.

The key objective of this Special Issue is to compile a collection of articles that illustrate new developments and findings in the stabilization and tracking control of fractional-order systems. In this Special Issue, significant attention will be dedicated to discovering novel approaches, highlighting notable innovations in both the theoretical foundations and practical applications of fractional-order systems.

Dr. Sakthivel Ramalingam
Dr. Parivallal Arumugam
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • robust control of fractional-order cyber–physical systems
  • tracking control of fractional-order systems
  • stabilization of fractional-order systems
  • fractional-order time delay systems
  • disturbance rejection of fractional order systems
  • optimal control of fractional-order systems
  • event-triggered control for fractional order systems
  • fractional-order networked control systems
  • fractional-order neural networks
  • fractional-order fuzzy systems

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Published Papers (3 papers)

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12 pages, 326 KiB  
Article
Observer Design for Fractional-Order Polynomial Fuzzy Systems Depending on a Parameter
by Hamdi Gassara, Mohamed Rhaima, Lassaad Mchiri and Abdellatif Ben Makhlouf
Fractal Fract. 2024, 8(12), 693; https://doi.org/10.3390/fractalfract8120693 - 25 Nov 2024
Cited by 1 | Viewed by 576
Abstract
For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time, such as load or temperature, increase the complexity [...] Read more.
For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time, such as load or temperature, increase the complexity of the observer design. In view of the aforementioned factors, this paper investigates the observer design problem for a class of Fractional-Order Polynomial Fuzzy Systems (FORPSs) depending on a parameter. The Caputo–Hadamard derivative is considered in this study. First, we prove the practical Mittag-Leffler stability, using the Lyapunov methods, for the general case of Caputo–Hadamard Fractional-Order Systems (CHFOSs) depending on a parameter. Secondly, based on this stability theory, we design an observer for the considered class of FORPSs. The state estimation error is ensured to be practically generalized Mittag-Leffler stable by solving Sum Of Squares (SOSs) conditions using the developed SOSTOOLS. Full article
(This article belongs to the Special Issue New Developments in Tracking and Stabilization of Fractional-Order Systems)
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14 pages, 1115 KiB  
Article
Practical Stability of Observer-Based Control for Nonlinear Caputo–Hadamard Fractional-Order Systems
by Rihab Issaoui, Omar Naifar, Mehdi Tlija, Lassaad Mchiri and Abdellatif Ben Makhlouf
Fractal Fract. 2024, 8(9), 531; https://doi.org/10.3390/fractalfract8090531 - 11 Sep 2024
Cited by 4 | Viewed by 709
Abstract
This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture complex dynamics, ensuring their practical stability remains a significant challenge. We [...] Read more.
This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture complex dynamics, ensuring their practical stability remains a significant challenge. We propose a novel concept of practical stability tailored to nonlinear Hadamard fractional-order systems, which guarantees that the system solutions converge to a small ball containing the origin, thereby enhancing their robustness against perturbations. Furthermore, we introduce a practical observer design that extends the classical observer framework to fractional-order systems under an enhanced One-Sided Lipschitz (OSL) condition. This extended OSL condition ensures the convergence of the proposed practical observer, even in the presence of significant nonlinearities and disturbances. Notably, the novelty of our approach lies in the extension of both the practical observer and the stability criteria, which are innovative even in the integer-order case. Theoretical results are substantiated through numerical examples, demonstrating the feasibility of the proposed method in real-world control applications. Our contributions pave the way for the development of robust observers in fractional-order systems, with potential applications across various engineering domains. Full article
(This article belongs to the Special Issue New Developments in Tracking and Stabilization of Fractional-Order Systems)
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24 pages, 346 KiB  
Article
Existence of Solutions for Caputo Sequential Fractional Differential Inclusions with Nonlocal Generalized Riemann–Liouville Boundary Conditions
by Murugesan Manigandan, Saravanan Shanmugam, Mohamed Rhaima and Elango Sekar
Fractal Fract. 2024, 8(8), 441; https://doi.org/10.3390/fractalfract8080441 - 26 Jul 2024
Viewed by 1109
Abstract
In this study, we explore the existence and uniqueness of solutions for a boundary value problem defined by coupled sequential fractional differential inclusions. This investigation is augmented by the introduction of a novel set of generalized Riemann–Liouville boundary conditions. Utilizing Carathéodory functions and [...] Read more.
In this study, we explore the existence and uniqueness of solutions for a boundary value problem defined by coupled sequential fractional differential inclusions. This investigation is augmented by the introduction of a novel set of generalized Riemann–Liouville boundary conditions. Utilizing Carathéodory functions and Lipschitz mappings, we establish existence results for these nonlocal boundary conditions. Utilizing fixed-point theorems designed for multi-valued maps, we obtain significant existence results for the problem, considering both convex and non-convex values. The derived results are clearly demonstrated with an illustrative example. Numerical examples are provided to validate the theoretical conclusions, contributing to a deeper understanding of fractional-order boundary value problems. Full article
(This article belongs to the Special Issue New Developments in Tracking and Stabilization of Fractional-Order Systems)
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