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Fractal Fract
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General Operators of Non-Integer Order in Modelling and Control of...
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General Operators of Non-Integer Order in Modelling and Control of Dynamical Systems

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

Deadline for manuscript submissions: closed (18 February 2022) | Viewed by 4685

Special Issue Editors

Dr. Aldo Jonathan Muñoz–Vázquez

E-Mail Website
Guest Editor
Department of Multidisciplinay Engineering, Texas A&M University, 6200 Tres Lagos Blvd, Higher Education Center at McAllen, McAllen, TX 78504, USA
Interests: fractional calculus; nonlinear systems; robotics; fuzzy logics; neural networks; control theory; integral equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Guillermo Fernández-Anaya

E-Mail Website
Guest Editor
Department of Physics and Mathematics, Universidad Iberoamericana, Ciudad de México 01219, Mexico
Interests: fractional calculus; linear systems theory; transport phenomena; condensed matter physics; control theory; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

When studying a broad class of physical systems and engineering processes, it is desirable to account for a good degree of generality in order to encompass as much as possible all the properties of the system dynamics, and to obtain more accurate and flexible structures. In this sense, different modelling approaches have been considered to understand the complexity of nature.

Fractional calculus arises as a generalisation of conventional integer-order calculus by proposing and studying integro-differential operators of fractional order. At present, further generalisations are available to study a larger class of dynamical systems, with more intricate responses. For instance, distributed-order derivatives and integrals make it possible to model dynamical systems that are composed of different elements of different orders, which are distributed on a certain interval, and variable-order operators permit the study of dynamical systems whose orders change with time. Additional generalisations are possible with Prabhakar fractional operators, and with Sonine-like generalised operators, among other possible approaches based on a wide variety of non-integer-order operators. Additionally, Marchaud–Sonine derivatives allow consideration of functions which are not necessarily differentiable.

A general way of representing a larger class of dynamical systems consists of expressing their dynamic equations in the form of well-suited integral equations with the most appropriate operators for the particular system under study. Such representation makes it possible to formulate control, observation, and/or modelling problems from a new perspective, and in some cases, to solve open problems, thus reflecting on dynamical systems with non-smooth effects and feedback stabilisation methodologies.

The purpose of this Special Issue is to present the latest studies and applications of the theory of general operators of non-integer order, for both modelling and control design. Manuscripts related, but not limited, to the stability analysis, modelling, control, and design of dynamical systems of non-integer order are welcome. Researchers in these fields are invited to contribute their original unpublished works. Both research and review papers are welcome.

Dr. Aldo Jonathan Muñoz–Vázquez
Prof. Dr. Guillermo Fernández-Anaya
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

  • fractional calculus
  • distributed-order calculus
  • variable-order calculus
  • generalised calculus
  • integral equations
  • stability analysis
  • chaotic systems
  • fractional-order control
  • fractional sliding mode control 
  • fractional fuzzy control
  • fractional neural networks

Published Papers (2 papers)

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19 pages, 624 KiB  
Article
Fixed-Time Fractional-Order Global Sliding Mode Control for Nonholonomic Mobile Robot Systems under External Disturbances
by Moussa Labbadi, Sahbi Boubaker, Mohamed Djemai, Souad Kamel Mekni and Abdelghani Bekrar
Fractal Fract. 2022, 6(4), 177; https://doi.org/10.3390/fractalfract6040177 - 22 Mar 2022
Cited by 16 | Viewed by 2246
Abstract
The present study addresses the problem of fixed-time stabilization (FTS) of mobile robots (MRs). The study’s distinguishing aspects are that the system under examination is subjected to external disturbances, and the system states are pushed to zero in a finite time. This paper [...] Read more.
The present study addresses the problem of fixed-time stabilization (FTS) of mobile robots (MRs). The study’s distinguishing aspects are that the system under examination is subjected to external disturbances, and the system states are pushed to zero in a finite time. This paper suggests new control techniques for chained-form nonholonomic systems (CFNS) subjected to disturbances. First, a switching fractional-order (FO) control approach is proposed for a first-order subsystem (FOS) of an MR under complex disturbances. Secondly, an FO generic global sliding mode control approach is designed for the second-order system (SOS) of the MR in the presence of disturbances. The suggested sliding manifold for the SOS of the MR guarantees global system stability and reduces the chattering problem during control operations. A conventional quadratic Lyapunov function (QLF) is used to converge to the origin in a finite time (FnT). Through this study, a stabilizer for an MR in the presence of disturbances based on an FO switching time-varying controller that can stabilize immeasurable states in a fixed time is proposed. Finally, three case simulations are provided to demonstrate the efficacy of the control strategy proposed in this work against external disturbances. Full article
(This article belongs to the Special Issue General Operators of Non-Integer Order in Modelling and Control of Dynamical Systems)
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25 pages, 8703 KiB  
Article
Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural Networks Incorporating Delays
by Peiluan Li, Jinling Yan, Changjin Xu and Youlin Shang
Fractal Fract. 2022, 6(3), 161; https://doi.org/10.3390/fractalfract6030161 - 15 Mar 2022
Cited by 8 | Viewed by 1682
Abstract
In this manuscript, we principally probe into a class of fractional-order tri-neuron neural networks incorporating delays. Making use of fixed point theorem, we prove the existence and uniqueness of solution to the fractional-order tri-neuron neural networks incorporating delays. By virtue of a suitable [...] Read more.
In this manuscript, we principally probe into a class of fractional-order tri-neuron neural networks incorporating delays. Making use of fixed point theorem, we prove the existence and uniqueness of solution to the fractional-order tri-neuron neural networks incorporating delays. By virtue of a suitable function, we prove the uniformly boundedness of the solution to the fractional-order tri-neuron neural networks incorporating delays. With the aid of the stability theory and bifurcation knowledge of fractional-order differential equation, a new delay-independent condition to guarantee the stability and creation of Hopf bifurcation of the fractional-order tri-neuron neural networks incorporating delays is established. Taking advantage of the mixed controller that contains state feedback and parameter perturbation, the stability region and the time of onset of Hopf bifurcation of the fractional-order trineuron neural networks incorporating delays are successfully controlled. Software simulation plots are displayed to illustrate the established key results. The obtained conclusions in this article have important theoretical significance in designing and controlling neural networks. Full article
(This article belongs to the Special Issue General Operators of Non-Integer Order in Modelling and Control of Dynamical Systems)
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