Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 3848

Special Issue Editors


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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
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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
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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
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Department of Electrical Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342 037, India
Interests: fractional-order systems; large scale systems; sliding mode control; large size nuclear reactor modelling and control

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Guest Editor
School of Mechanical and Electrical Engineering, Soochow University, Suzhou 215137, China
Interests: nonlinear systems and control; stochastic systems; multi-agent systems; fault diagnosis and reliable control; interval observer design
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Special Issue Information

Dear Colleagues,

Over the last two decades, (fractional) differential equations have become more common in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry, and many other fields, allowing for a new and more realistic way to capture memory-dependent phenomena and irregularities within systems through more sophisticated mathematical analysis. As a result of its growing applications, the study of the stability of (fractional) differential equations has received significant attention. Furthermore, in recent years, interest in fractional- and integer-order controllers has grown. Examples of these are optimal control, CRONE controllers, fractional PID controllers, lead–lag compensators, and sliding mode control. 

The purpose of this Special Issue is to disseminate research on fractional-/integer-order control theory and its applications in practical systems modeled using fractional-/integer-order differential equations. These include the design, implementation, and application of fractional-/integer-order control to electrical circuits and systems, mechanical systems, chemical systems, biological systems, finance systems, and so on.

Submissions are welcome on, but not limited to, the following topics:

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

Dr. Thach Ngoc Dinh
Dr. Shyam Kamal
Dr. Rajesh Kumar Pandey
Prof. Dr. Bijnan Bandyopadhyay
Prof. Dr. Jun Huang
Guest Editors

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Related Special Issue

Published Papers (3 papers)

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Research

22 pages, 3931 KiB  
Article
Dynamic Event-Triggered Prescribed-Time Consensus Tracking of Nonlinear Time-Delay Multiagent Systems by Output Feedback
by Sung Jin Yoo and Bong Seok Park
Fractal Fract. 2024, 8(9), 545; https://doi.org/10.3390/fractalfract8090545 - 19 Sep 2024
Viewed by 583
Abstract
Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore, designing a dynamic event-triggering mechanism is crucial to ensuring PT [...] Read more.
Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore, designing a dynamic event-triggering mechanism is crucial to ensuring PT stability, even in the presence of unknown time delays. This article focuses on developing a dynamic event-triggering mechanism to achieve adaptive practical PT output-feedback consensus tracking for nonlinear uncertain multiagent systems with unknown time delays. Firstly, a delay-independent PT state observer using a time-varying gain function is designed to estimate the immeasurable states. Following this, a novel distributed delay-independent PT consensus tracking scheme is constructed, incorporating a dynamic event-triggered mechanism through the command-filtered backstepping approach. In this design, dynamic variables based on a time-varying gain function are developed to support the event-triggering mechanism, ensuring practical stability within the prescribed settling time. Consequently, the proposed output-feedback control protocol can achieve practical PT stability, meaning that consensus tracking errors are constrained to a neighborhood around zero within a pre-specified time, regardless of the initial states of the agents or design parameters, while also avoiding the Zeno phenomenon. Finally, the effectiveness of the proposed strategy is validated through an illustrative example, which includes a comparative analysis. Full article
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17 pages, 581 KiB  
Article
Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance
by Xiaoli Yang, Jing Li, Shuzhi (Sam) Ge, Xiaoling Liang and Tao Han
Fractal Fract. 2024, 8(6), 339; https://doi.org/10.3390/fractalfract8060339 - 5 Jun 2024
Viewed by 880
Abstract
In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does [...] Read more.
In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does not depend on the accurate initial value of the error signal and has the ability of fixed-time convergence, is proposed for the first time. A radial basis function neural network is introduced to identify unknown nonlinear functions, and the characteristic of Gaussian basis functions is utilized to overcome the difficulties of the nonstrict-feedback structure. Moreover, in contrast to the traditional Backstepping technique, a command filter-based adaptive control algorithm is constructed, which solves the “explosion of complexity” problem and relaxes the assumption on the reference signal. Additionally, it is guaranteed that the tracking error falls within a prescribed small neighborhood by the designed performance functions in fixed time, and the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed control scheme is verified by numerical simulation. Full article
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21 pages, 5607 KiB  
Article
An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer
by Ali Yüce
Fractal Fract. 2023, 7(6), 460; https://doi.org/10.3390/fractalfract7060460 - 3 Jun 2023
Cited by 2 | Viewed by 1694
Abstract
System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical [...] Read more.
System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model. Full article
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