Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 8267

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State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
Interests: fractional-order systems; nonlinear systems; multi-agent systems; prescribed performance control; nonlinear control
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Guest Editor
Institut National des Sciences Appliquées Centre Val de Loire, Bourges, France
Interests: non-asymptotic state estimation; non-asymptotic fractional order differentiator
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INSA Centre Val de Loire, Université d’Orléans, PRISME EA 4229, CEDEX, 18022 Bourges, France
Interests: estimation and control for fractional order systems; numerical solutions for fractional order differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over recent years, a growing number of authors’ works from various science and engineering fields have dealt with dynamical systems, described by the connection between the theory of artificial intelligence and fractional differential equations, and many computational fractional intelligence systems and stability analysis and image processing applications have been proposed. The aim of this Special Issue is to gather articles reflecting the latest developments in applied mathematics and advanced intelligent control engineering related to the interdisciplinary topics of control, fractional calculus, image processing, and their applications in engineering science.

Fractional calculus and fractional processes, with applications in control systems and image processing, represent a hot topic. Fractional order systems are a natural generalization of classical integer order systems with the capacity to accurately describe many real-world physical systems. The fusion and noise suppression of medical images have become increasingly difficult to ignore in image processing, and these techniques provide abundant information for clinical diagnosis and treatment. Image fusion is a significant factor in image processing owing to the increase in image acquisition models. Recently, fractional operators have played an important role in image processing. Additionally, powerful fractional operating tools have been introduced, possessing extensive applications in the analysis and design of nonlinear control systems. Singular systems are governed by so-called singular differential equations, endowing the systems with many special features not found in classical systems. The approaches of fractional order control systems, which borrow from those of integer order control systems, are attracting increasing attention within the control field.

We invite the submission of high-quality articles in this field by researchers and experts in academia and industry.

Dr. Jin-Xi Zhang
Dr. Xuefeng Zhang
Prof. Dr. Driss Boutat
Dr. Da-Yan Liu
Guest Editors

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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

  • image processing
  • image fusion
  • image denoising
  • image enhancement
  • analysis and control of fractional systems
  • singular fractional systems
  • intelligent fractional ​control
  • high-performance control
  • non-asymptotic fractional state estimation
  • fractional numerical solution and simulation​

Published Papers (8 papers)

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Research

29 pages, 10726 KiB  
Article
Crop and Weed Segmentation and Fractal Dimension Estimation Using Small Training Data in Heterogeneous Data Environment
by Rehan Akram, Jin Seong Hong, Seung Gu Kim, Haseeb Sultan, Muhammad Usman, Hafiz Ali Hamza Gondal, Muhammad Hamza Tariq, Nadeem Ullah and Kang Ryoung Park
Fractal Fract. 2024, 8(5), 285; https://doi.org/10.3390/fractalfract8050285 - 10 May 2024
Viewed by 554
Abstract
The segmentation of crops and weeds from camera-captured images is a demanding research area for advancing agricultural and smart farming systems. Previously, the segmentation of crops and weeds was conducted within a homogeneous data environment where training and testing data were from the [...] Read more.
The segmentation of crops and weeds from camera-captured images is a demanding research area for advancing agricultural and smart farming systems. Previously, the segmentation of crops and weeds was conducted within a homogeneous data environment where training and testing data were from the same database. However, in the real-world application of advancing agricultural and smart farming systems, it is often the case of a heterogeneous data environment where a system trained with one database should be used for testing with a different database without additional training. This study pioneers the use of heterogeneous data for crop and weed segmentation, addressing the issue of degraded accuracy. Through adjusting the mean and standard deviation, we minimize the variability in pixel value and contrast, enhancing segmentation robustness. Unlike previous methods relying on extensive training data, our approach achieves real-world applicability with just one training sample for deep learning-based semantic segmentation. Moreover, we seamlessly integrated a method for estimating fractal dimensions into our system, incorporating it as an end-to-end task to provide important information on the distributional characteristics of crops and weeds. We evaluated our framework using the BoniRob dataset and the CWFID. When trained with the BoniRob dataset and tested with the CWFID, we obtained a mean intersection of union (mIoU) of 62% and an F1-score of 75.2%. Furthermore, when trained with the CWFID and tested with the BoniRob dataset, we obtained an mIoU of 63.7% and an F1-score of 74.3%. We confirmed that these values are higher than those obtained by state-of-the-art methods. Full article
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17 pages, 1719 KiB  
Article
Adaptive Fractional-Order Multi-Scale Optimization TV-L1 Optical Flow Algorithm
by Qi Yang, Yilu Wang, Lu Liu and Xiaomeng Zhang
Fractal Fract. 2024, 8(4), 179; https://doi.org/10.3390/fractalfract8040179 - 22 Mar 2024
Cited by 1 | Viewed by 782
Abstract
We propose an adaptive fractional multi-scale optimization optical flow algorithm, which for the first time improves the over-smoothing of optical flow estimation under the total variation model from the perspective of global feature and local texture balance, and solves the problem that the [...] Read more.
We propose an adaptive fractional multi-scale optimization optical flow algorithm, which for the first time improves the over-smoothing of optical flow estimation under the total variation model from the perspective of global feature and local texture balance, and solves the problem that the convergence of fractional optical flow algorithms depends on the order parameter. Specifically, a fractional-order discrete L1-regularization Total Variational Optical Flow model is constructed. On this basis, the Ant Lion algorithm is innovatively used to realize the iterative calculation of the optical flow equation, and the fractional order is dynamically adjusted to obtain an adaptive optimization algorithm with strong search accuracy and high efficiency. In this paper, the flexibility of optical flow estimation in weak gradient texture scenes is increased, and the optical flow extraction rate of target features at multiple scales is greatly improved. We show excellent recognition performance and stability under the MPI_Sintel and Middlebury benchmarks. Full article
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25 pages, 4925 KiB  
Article
Backstepping Control with a Fractional-Order Command Filter and Disturbance Observer for Unmanned Surface Vehicles
by Runan Ma, Jian Chen, Chengxing Lv, Zhibo Yang and Xiangyu Hu
Fractal Fract. 2024, 8(1), 23; https://doi.org/10.3390/fractalfract8010023 - 27 Dec 2023
Viewed by 1035
Abstract
In the paper, a backstepping control strategy based on a fractional-order finite-time command filter and a fractional-order finite-time disturbance observer is proposed for the trajectory tracking control of an unmanned surface vehicle. A fractional-order finite-time command filter is presented to estimate the derivatives [...] Read more.
In the paper, a backstepping control strategy based on a fractional-order finite-time command filter and a fractional-order finite-time disturbance observer is proposed for the trajectory tracking control of an unmanned surface vehicle. A fractional-order finite-time command filter is presented to estimate the derivatives of the intermediate control, which cannot be directly calculated, thereby reducing the chattering generated by the integer-order command filter. The fractional-order finite-time disturbance observer is presented to approximate and compensate for the model uncertainty and unknown external disturbances in the system. Subsequently, the globally asymptotically stable nature of the closed-loop system is proved based on the Lyapunov method. The effectiveness of the method is proven by simulation experiments on unmanned surface vehicles. Full article
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16 pages, 1075 KiB  
Article
Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers
by Kai-Di Xu and Jin-Xi Zhang
Fractal Fract. 2023, 7(8), 594; https://doi.org/10.3390/fractalfract7080594 - 1 Aug 2023
Cited by 3 | Viewed by 770
Abstract
This paper is concerned with the tracking control problem for the lower-triangular systems with unknown fractional powers and nonparametric uncertainties. A prescribed performance control approach is put forward as a means of resolving this problem. The proposed control law incorporates a set of [...] Read more.
This paper is concerned with the tracking control problem for the lower-triangular systems with unknown fractional powers and nonparametric uncertainties. A prescribed performance control approach is put forward as a means of resolving this problem. The proposed control law incorporates a set of barrier functions to guarantee error constraints. Unlike the previous works, our approach works for the cases where the fractional powers, the nonlinearities, and their bounding functions or bounds are totally unknown; no restrictive conditions on the powers, such as power order restriction, specific size limitation or homogeneous condition, are made. Moreover, neither the powers and system nonlinearities nor their bounding functions or bounds are needed. It achieves reference tracking with the preassigned tracking accuracy and convergence speed. In addition, our controller is simple, as it does not necessitate parameter identification, function approximation, derivative calculation, or adding a power integrator technique. At the end, a comparative simulation demonstrates the effectiveness and advantage of the proposed approach. Full article
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13 pages, 620 KiB  
Article
Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < α < 2
by Ying Di, Jin-Xi Zhang and Xuefeng Zhang
Fractal Fract. 2023, 7(8), 577; https://doi.org/10.3390/fractalfract7080577 - 27 Jul 2023
Cited by 3 | Viewed by 794
Abstract
The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. [...] Read more.
The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results. Full article
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14 pages, 511 KiB  
Article
A Finite-Dimensional Control Scheme for Fractional-Order Systems under Denial-of-Service Attacks
by Ying Zou, Xinyao Li, Chao Deng and Xiaowen Wu
Fractal Fract. 2023, 7(7), 562; https://doi.org/10.3390/fractalfract7070562 - 21 Jul 2023
Viewed by 775
Abstract
In this article, the security control problem of discrete-time fractional-order networked systems under denial-of-service (DoS) attacks is considered. A practically applicable finite-dimensional control strategy will be developed for fractional-order systems that possess nonlocal characteristics. By employing the Lyapunov method, it is theoretically proved [...] Read more.
In this article, the security control problem of discrete-time fractional-order networked systems under denial-of-service (DoS) attacks is considered. A practically applicable finite-dimensional control strategy will be developed for fractional-order systems that possess nonlocal characteristics. By employing the Lyapunov method, it is theoretically proved that under the proposed controller, the obtained closed-loop fractional system is globally input-to-state stable (ISS), even in the presence of DoS attacks. Finally, the effectiveness of the designed control method is demonstrated by the numerical example. Full article
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21 pages, 9915 KiB  
Article
Depth Image Enhancement Algorithm Based on Fractional Differentiation
by Tingsheng Huang, Xinjian Wang, Da Xie, Chunyang Wang and Xuelian Liu
Fractal Fract. 2023, 7(5), 394; https://doi.org/10.3390/fractalfract7050394 - 11 May 2023
Cited by 3 | Viewed by 1133
Abstract
Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image-enhancement methods, which are typically based on integer-order calculus, cannot exploit the textural information of an image, and their enhancement effect is limited. To solve this problem, [...] Read more.
Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image-enhancement methods, which are typically based on integer-order calculus, cannot exploit the textural information of an image, and their enhancement effect is limited. To solve this problem, fractional differentiation has been introduced as an innovative image-processing tool. It enables the flexible use of local and non-local information by taking into account the continuous changes between orders, thereby improving the enhancement effect. In this study, a fractional differential is applied in depth image enhancement and used to establish a novel algorithm, named the fractional differential-inverse-distance-weighted depth image enhancement method. Experiments are performed to verify the effectiveness and universality of the algorithm, revealing that it can effectively solve edge and hole interference and significantly enhance textural details. The effects of the order of fractional differentiation and number of iterations on the enhancement performance are examined, and the optimal parameters are obtained. The process data of depth image enhancement associated with the optimal number of iterations and fractional order are expected to facilitate depth image enhancement in actual scenarios. Full article
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20 pages, 943 KiB  
Article
Generalized Criteria for Admissibility of Singular Fractional Order Systems
by Longxin Zhang, Jin-Xi Zhang and Xuefeng Zhang
Fractal Fract. 2023, 7(5), 363; https://doi.org/10.3390/fractalfract7050363 - 28 Apr 2023
Cited by 1 | Viewed by 1079
Abstract
Unified frameworks for fractional order systems with fractional order 0<α<2 are worth investigating. The aim of this paper is to provide a unified framework for stability and admissibility for fractional order systems and singular fractional order systems with [...] Read more.
Unified frameworks for fractional order systems with fractional order 0<α<2 are worth investigating. The aim of this paper is to provide a unified framework for stability and admissibility for fractional order systems and singular fractional order systems with 0<α<2, respectively. By virtue of the LMI region and GLMI region, five stability theorems are presented. Two admissibility theorems for singular fractional order systems are extended from Theorem 5, and, in particular, a strict LMI stability criterion involving the least real decision variables without equality constraint by isomorphic mapping and congruent transform. The equivalence between the admissibility Theorems 6 and 7 is derived. The proposed framework contains some other existing results in the case of 1α<2 or 0<α<1. Compared with published unified frameworks, the proposed framework is truly unified and does not require additional conditional assignment. Finally, without loss of generality, a unified control law is designed to make the singular feedback system admissible based on the criterion in a strict LMI framework and demonstrated by two numerical examples. Full article
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