Special Issue "Fractional-Order System: Control Theory and Applications"

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

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 4039

Special Issue Editors

Dr. Thach Ngoc Dinh
E-Mail Website
Guest Editor
Conservatoire National des Arts et Métiers (CNAM), Cedric-Laetitia, 292 Rue St-Martin, 75141 Paris Cedex 03, France
Interests: state estimation; interval observer; robust control; output feedback; positive fractional-order systems
Dr. Shyam Kamal
E-Mail Website
Guest Editor
Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, India
Interests: stability and stabilization of fractional order systems; sliding mode control; nonlinear observers; contraction analysis
Dr. Rajesh Kumar Pandey
E-Mail Website
Guest Editor
Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
Interests: fractional differential equations; fractional variational problems; applications of fractional calculus in image processing; computational methods

Special Issue Information

Dear Colleagues,

In the last two decades, fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry, and many other fields, opening a new and more realistic way to capture memory-dependent phenomena and irregularities inside systems using more sophisticated mathematical analysis.

As a result of the growing applications, the study of stability of fractional differential equations has attracted much attention. Furthermore, in recent years, an increasing amount of attention has been given to fractional-order controllers. Some of these applications include optimal control, CRONE controllers, fractional PID controllers, lead-lag compensators, and sliding mode control.

The focus of this Special Issue is to continue to advance research on topics relating to fractional-order control theory and its applications to practical systems modeled using fractional-order differential equations such as design, implementation, and application of fractional-order control to electrical circuits and systems, mechanical systems, chemical systems, biological systems, finance systems, etc.

Topics that are invited for submission include (but are not limited to):

  • Fractional-order control theory for fractional-order systems;
  • Fractional-order control theory for integer-order systems
  • Lyapunov-based stability and stabilization of fractional-order systems;
  • Feedback linearization-based controller and observer design for fractional-order systems;
  • Digital implementation of fractional-order control;
  • Sliding mode control of fractional-order systems;
  • Finite, fixed, and predefined-time stability and stabilization of fractional-order systems;
  • Interval observer and set-membership design for fractional-order systems;
  • High-gain based observers and differentiator design for fractional-order systems;
  • Event-based control of fractional-order systems;
  • Incremental stability of fractional-order systems;
  • Control of non-minimum phase systems using fractional-order theory;
  • New physical interpretation of fractional-order operators and their relationship to control design;
  • Design and development of efficient battery management and state of heath estimation using fractional-order calculus;
  • Applications of fractional-order control to electrical, mechanical, chemical, finance, and biological systems;
  • Verification and reachability analysis of fractional-order differential equations.

Dr. Thach Ngoc Dinh
Dr. Shyam Kamal
Dr. Rajesh Kumar Pandey
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 1800 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-order control theory
  • Fractional-order controllers, observers, and differentiator design
  • Event-based control of fractional-order systems
  • Lyapunov analysis of fractional-order differential equations
  • Fractional differential equations
  • Fractional variational problems and fractional control problems
  • Analytical and computational methods for fractional-order systems

Published Papers (6 papers)

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Research

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Article
Finite Difference–Collocation Method for the Generalized Fractional Diffusion Equation
Fractal Fract. 2022, 6(7), 387; https://doi.org/10.3390/fractalfract6070387 - 11 Jul 2022
Viewed by 291
Abstract
In this paper, an approximate method combining the finite difference and collocation methods is studied to solve the generalized fractional diffusion equation (GFDE). The convergence and stability analysis of the presented method are also established in detail. To ensure the effectiveness and the [...] Read more.
In this paper, an approximate method combining the finite difference and collocation methods is studied to solve the generalized fractional diffusion equation (GFDE). The convergence and stability analysis of the presented method are also established in detail. To ensure the effectiveness and the accuracy of the proposed method, test examples with different scale and weight functions are considered, and the obtained numerical results are compared with the existing methods in the literature. It is observed that the proposed approach works very well with the generalized fractional derivatives (GFDs), as the presence of scale and weight functions in a generalized fractional derivative (GFD) cause difficulty for its discretization and further analysis. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
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Article
Fractional-Order Interval Observer for Multiagent Nonlinear Systems
Fractal Fract. 2022, 6(7), 355; https://doi.org/10.3390/fractalfract6070355 - 25 Jun 2022
Viewed by 333
Abstract
A framework of distributed interval observers is introduced for fractional-order multiagent systems in the presence of nonlinearity. First, a frame was designed to construct the upper and lower bounds of the system state. By using monotone system theory, the positivity of the error [...] Read more.
A framework of distributed interval observers is introduced for fractional-order multiagent systems in the presence of nonlinearity. First, a frame was designed to construct the upper and lower bounds of the system state. By using monotone system theory, the positivity of the error dynamics could be ensured, which implies that the bounds could trap the original state. Second, a sufficient condition was applied to guarantee the boundedness of distributed interval observers. Then, an extension of Lyapunov function in the fractional calculus field was the basis of the sufficient condition. An algorithm associated with the procedure of the observer design is also provided. Lastly, a numerical simulation is used to demonstrate the effectiveness of the distributed interval observer. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
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Article
Finite Time Stability of Fractional Order Systems of Neutral Type
Fractal Fract. 2022, 6(6), 289; https://doi.org/10.3390/fractalfract6060289 - 26 May 2022
Viewed by 527
Abstract
This work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is [...] Read more.
This work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is the application of fixed point theory to show the FTS of NFOTSs. Finally, using two examples, the theoretical contributions are confirmed and substantiated. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
Article
Design and Application of an Interval Estimator for Nonlinear Discrete-Time SEIR Epidemic Models
Fractal Fract. 2022, 6(4), 213; https://doi.org/10.3390/fractalfract6040213 - 09 Apr 2022
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Abstract
This paper designs an interval estimator for a fourth-order nonlinear susceptible-exposed-infected-recovered (SEIR) model with disturbances using noisy counts of susceptible people provided by Public Health Services (PHS). Infectious diseases are considered the main cause of deaths among the top ten worldwide, as per [...] Read more.
This paper designs an interval estimator for a fourth-order nonlinear susceptible-exposed-infected-recovered (SEIR) model with disturbances using noisy counts of susceptible people provided by Public Health Services (PHS). Infectious diseases are considered the main cause of deaths among the top ten worldwide, as per the World Health Organization (WHO). Therefore, tracking and estimating the evolution of these diseases are important to make intervention strategies. We study a real case in which some uncertain variables such as model disturbances, uncertain input and output measurement noise are not exactly available but belong to an interval. Moreover, the uncertain transmission bound rate from the susceptible towards the exposed stage is not available for measurement. We designed an interval estimator using an observability matrix that generates a tight interval vector for the actual states of the SEIR model in a guaranteed way without computing the observer gain. As the developed approach is not dependent on observer gain, our method provides more freedom. The convergence of the width to a known value in finite time is investigated for the estimated state vector to prove the stability of the estimation error, significantly improving the accuracy for the proposed approach. Finally, simulation results demonstrate the satisfying performance of the proposed algorithm. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
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Article
Multiweighted-Type Fractional Fourier Transform: Unitarity
Fractal Fract. 2021, 5(4), 205; https://doi.org/10.3390/fractalfract5040205 - 08 Nov 2021
Viewed by 446
Abstract
The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform [...] Read more.
The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
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Review

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Review
A Review of Recent Developments in Autotuning Methods for Fractional-Order Controllers
Fractal Fract. 2022, 6(1), 37; https://doi.org/10.3390/fractalfract6010037 - 11 Jan 2022
Cited by 2 | Viewed by 540
Abstract
The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID. Several versions of this controller have been proposed, including different tuning methods and implementation possibilities. Quite [...] Read more.
The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID. Several versions of this controller have been proposed, including different tuning methods and implementation possibilities. Quite a few recent papers discuss the practical use of such controllers. However, the industrial acceptance of these controllers is still far from being reached. Autotuning methods for such fractional order PIDs could possibly make them more appealing to industrial applications, as well. In this paper, the current autotuning methods for fractional order PIDs are reviewed. The focus is on the most recent findings. A comparison between several autotuning approaches is considered for various types of processes. Numerical examples are given to highlight the practicality of the methods that could be extended to simple industrial processes. Full article
(This article belongs to the Special Issue Fractional-Order System: Control Theory and Applications)
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