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

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 16065

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Special Issue Editors

Dr. Jinxi Zhang

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Guest Editor

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
Special Issues, Collections and Topics in MDPI journals

Dr. Xuefeng Zhang

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Guest Editor

College of Sciences, Northeastern University, Shengyang 110819, China
Interests: singular systems; fractional systems; robust control
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Driss Boutat

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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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Dr. Dayan Liu

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Guest Editor

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

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

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

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Published Papers (14 papers)

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Research

26 pages, 33294 KiB

Open AccessArticle

RGB-D Camera and Fractal-Geometry-Based Maximum Diameter Estimation Method of Apples for Robot Intelligent Selective Graded Harvesting

by Bin Yan and Xiameng Li

Fractal Fract. 2024, 8(11), 649; https://doi.org/10.3390/fractalfract8110649 - 7 Nov 2024

Viewed by 376

Abstract

Realizing the integration of intelligent fruit picking and grading for apple harvesting robots is an inevitable requirement for the future development of smart agriculture and precision agriculture. Therefore, an apple maximum diameter estimation model based on RGB-D camera fusion depth information was proposed in the study. Firstly, the maximum diameter parameters of Red Fuji apples were collected, and the results were statistically analyzed. Then, based on the Intel RealSense D435 RGB-D depth camera and LabelImg software, the depth information of apples and the two-dimensional size information of fruit images were obtained. Furthermore, the relationship between fruit depth information, two-dimensional size information of fruit images, and the maximum diameter of apples was explored. Based on Origin software, multiple regression analysis and nonlinear surface fitting were used to analyze the correlation between fruit depth, diagonal length of fruit bounding rectangle, and maximum diameter. A model for estimating the maximum diameter of apples was constructed. Finally, the constructed maximum diameter estimation model was experimentally validated and evaluated for imitation apples in the laboratory and fruits on the Red Fuji fruit trees in modern apple orchards. The experimental results showed that the average maximum relative error of the constructed model in the laboratory imitation apple validation set was ±4.1%, the correlation coefficient (R²) of the estimated model was 0.98613, and the root mean square error (RMSE) was 3.21 mm. The average maximum diameter estimation relative error on the modern orchard Red Fuji apple validation set was ±3.77%, the correlation coefficient (R²) of the estimation model was 0.84, and the root mean square error (RMSE) was 3.95 mm. The proposed model can provide theoretical basis and technical support for the selective apple-picking operation of intelligent robots based on apple size grading. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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32 pages, 8354 KiB

Open AccessArticle

Estimation of Fractal Dimension and Detection of Fake Finger-Vein Images for Finger-Vein Recognition

by Seung Gu Kim, Jin Seong Hong, Jung Soo Kim and Kang Ryoung Park

Fractal Fract. 2024, 8(11), 646; https://doi.org/10.3390/fractalfract8110646 - 31 Oct 2024

Viewed by 547

Abstract

With recent advancements in deep learning, spoofing techniques have developed and generative adversarial networks (GANs) have become an emerging threat to finger-vein recognition systems. Therefore, previous research has been performed to generate finger-vein images for training spoof detectors. However, these are limited and researchers still cannot generate elaborate fake finger-vein images. Therefore, we develop a new densely updated contrastive learning-based self-attention generative adversarial network (DCS-GAN) to create elaborate fake finger-vein images, enabling the training of corresponding spoof detectors. Additionally, we propose an enhanced convolutional network for a next-dimension (ConvNeXt)-Small model with a large kernel attention module as a new spoof detector capable of distinguishing the generated fake finger-vein images. To improve the spoof detection performance of the proposed method, we introduce fractal dimension estimation to analyze the complexity and irregularity of class activation maps from real and fake finger-vein images, enabling the generation of more realistic and sophisticated fake finger-vein images. Experimental results obtained using two open databases showed that the fake images by the DCS-GAN exhibited Frechet inception distances (FID) of 7.601 and 23.351, with Wasserstein distances (WD) of 18.158 and 10.123, respectively, confirming the possibility of spoof attacks when using existing state-of-the-art (SOTA) frameworks of spoof detection. Furthermore, experiments conducted with the proposed spoof detector yielded average classification error rates of 0.4% and 0.12% on the two aforementioned open databases, respectively, outperforming existing SOTA methods for spoof detection. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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34 pages, 12191 KiB

Open AccessArticle

Artificial Intelligence-Based Segmentation and Classification of Plant Images with Missing Parts and Fractal Dimension Estimation

by Ganbayar Batchuluun, Seung Gu Kim, Jung Soo Kim, Tahir Mahmood and Kang Ryoung Park

Fractal Fract. 2024, 8(11), 633; https://doi.org/10.3390/fractalfract8110633 - 27 Oct 2024

Viewed by 728

Abstract

Existing research on image-based plant classification has demonstrated high performance using artificial intelligence algorithms. However, limited camera viewing angles can cause parts of the plant to be invisible in the acquired images, leading to an inaccurate classification. However, this issue has not been addressed by previous research. Hence, our study aims to introduce a method to improve classification performance by taking these limitations into account; specifically, we incorporated both segmentation and classification networks structured as shallow networks to expedite the processing times. The proposed shallow plant segmentation network (Shal-PSN) performs adversarial learning based on a discriminator network; and a shallow plant classification network (Shal-PCN) with applied residual connections was also implemented. Moreover, the fractal dimension estimation is used in this study for analyzing the segmentation results. Additionally, this study evaluated the performance of the proposed Shal-PSN that achieved the dice scores (DSs) of 87.43% and 85.71% with PlantVillage and open leaf image (OLID-I) open datasets, respectively, in instances where 40–60% of plant parts were missing. Moreover, the results demonstrate that the proposed method increased the classification accuracy from 41.16% to 90.51% in the same instances. Overall, our approach achieved superior performance compared to the existing state-of-the-art classification methods. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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26 pages, 19476 KiB

Open AccessArticle

Fractal Dimension-Based Multi-Focus Image Fusion via Coupled Neural P Systems in NSCT Domain

by Liangliang Li, Xiaobin Zhao, Huayi Hou, Xueyu Zhang, Ming Lv, Zhenhong Jia and Hongbing Ma

Fractal Fract. 2024, 8(10), 554; https://doi.org/10.3390/fractalfract8100554 - 25 Sep 2024

Cited by 1 | Viewed by 788

Abstract

In this paper, we introduce an innovative approach to multi-focus image fusion by leveraging the concepts of fractal dimension and coupled neural P (CNP) systems in nonsubsampled contourlet transform (NSCT) domain. This method is designed to overcome the challenges posed by the limitations of camera lenses and depth-of-field effects, which often prevent all parts of a scene from being simultaneously in focus. Our proposed fusion technique employs CNP systems with a local topology-based fusion model to merge the low-frequency components effectively. Meanwhile, for the high-frequency components, we utilize the spatial frequency and fractal dimension-based focus measure (FDFM) to achieve superior fusion performance. The effectiveness of the method is validated through extensive experiments conducted on three benchmark datasets: Lytro, MFI-WHU, and MFFW. The results demonstrate the superiority of our proposed multi-focus image fusion method, showcasing its potential to significantly enhance image clarity across the entire scene. Our algorithm has achieved advantageous values on metrics

Q_{A B / F}

Q_{C B}

Q_{C V}

Q_{E}

Q_{F M I}

Q_{G}

Q_{M I}

, and

Q_{N C I E}

. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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32 pages, 7304 KiB

Open AccessArticle

Estimation of Fractal Dimension and Segmentation of Body Regions for Deep Learning-Based Gender Recognition

by Dong Chan Lee, Min Su Jeong, Seong In Jeong, Seung Yong Jung and Kang Ryoung Park

Fractal Fract. 2024, 8(10), 551; https://doi.org/10.3390/fractalfract8100551 - 24 Sep 2024

Viewed by 744

Abstract

There are few studies utilizing only IR cameras for long-distance gender recognition, and they have shown low recognition performance due to their lack of color and texture information in IR images with a complex background. Therefore, a rough body segmentation-based gender recognition network (RBSG-Net) is proposed, with enhanced gender recognition performance achieved by emphasizing the silhouette of a person through a body segmentation network. Anthropometric loss for the segmentation network and an adaptive body attention module are also proposed, which effectively integrate the segmentation and classification networks. To enhance the analytic capabilities of the proposed framework, fractal dimension estimation was introduced into the system to gain insights into the complexity and irregularity of the body region, thereby predicting the accuracy of body segmentation. For experiments, near-infrared images from the Sun Yat-sen University multiple modality re-identification version 1 (SYSU-MM01) dataset and thermal images from the Dongguk body-based gender version 2 (DBGender-DB2) database were used. The equal error rates of gender recognition by the proposed model were 4.320% and 8.303% for these two databases, respectively, surpassing state-of-the-art methods. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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19 pages, 44726 KiB

Open AccessArticle

Fractional-Order Modeling and Identification for an SCR Denitrification Process

by Wei Ai, Xinlei Lin, Ying Luo and Xiaowei Wang

Fractal Fract. 2024, 8(9), 524; https://doi.org/10.3390/fractalfract8090524 - 9 Sep 2024

Viewed by 596

Abstract

This paper presents an application of a fractional-order system on modeling an industrial process system with large inertia and time delay. The traditional integer-order model of the process system is extended to a fractional-order one in this work. To identify the parameters of the proposed fractional-order model, an output-error identification algorithm is presented. Based on the experimental step response data of the selective catalytic reduction (SCR) denitrification process in a power plant, this proposed fractional-order model shows a better fitting result compared with the typical integer-order models. An integer-order proportional–integral (PI) controller is designed for the process plant using a simple scheme according to the identified fractional-order and integer-order models, respectively. Validation tests are performed based on the obtained fractional-order and integer-order models, demonstrating the advantages of the proposed fractional-order model with the corresponding system identification approach for industrial processes with large inertia and time delay. Full article

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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29 pages, 10726 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 1341

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 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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17 pages, 1719 KiB

Open AccessArticle

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 2 | Viewed by 1310

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 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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25 pages, 4925 KiB

Open AccessArticle

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

Cited by 4 | Viewed by 1462

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 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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16 pages, 1075 KiB

Open AccessArticle

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 4 | Viewed by 1048

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 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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13 pages, 620 KiB

Open AccessArticle

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 8 | Viewed by 1068

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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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14 pages, 511 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 1040

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 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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21 pages, 9915 KiB

Open AccessArticle

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 4 | Viewed by 1564

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, 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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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20 pages, 943 KiB

Open AccessArticle

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 2 | Viewed by 1426

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

1 \leq α < 2

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

(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms)

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