Synchronization and Adaptive Control for Fractional-Order Network Systems

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

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 5906

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Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, School of Computer Science and Technology, Tiangong University, Tianjin 300387, China
Interests: complex networks; coupled neural networks; multiagent systems; fractional-order systems
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School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Interests: cluster intelligent decision-making; multiagent deep reinforcement learning; intelligent robot; fractional-order systems

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Faculty of Information Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing 100124, China
Interests: robust control and filtering; sampled-data control; distributed parameter systems; fuzzy modeling and control; fractional-order systems

Special Issue Information

Dear Colleagues,

Compared with integer calculus, fractional calculus not only has more freedom in modeling real complex systems, but it also possesses some noteworthy features, such as its genetic characteristics, infinite memory, and so on. Therefore, fractional-order networks can better describe the dynamic behaviors of real networks such as fractional-order multirobot systems, coupled fractional-order chaotic systems, coupled fractional-order neural networks, and so on. The objective of this Special Issue is to provide an opportunity for researchers globally to publish both original research and review articles with a focus on fractional-order network systems. Potential topics include, but are not limited to, the following:

  • Analysis and control for fractional-order neural networks;
  • Analysis and control for fractional-order reaction-diffusion neural networks;
  • Cooperative control of fractional-order multiagent systems;
  • Analysis and control for fractional-order complex networks;
  • Applications,

Prof. Dr. Jinliang Wang
Dr. Min Li
Prof. Dr. Zipeng Wang
Guest Editors

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Keywords

  • fractional-order neural networks
  • fractional-order reaction-diffusion neural networks
  • fractional-order multiagent systems
  • fractional-order complex networks
  • stability
  • synchronization
  • consensus
  • formation control

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Published Papers (4 papers)

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Research

15 pages, 868 KiB  
Article
Synchronization Control of Complex Spatio-Temporal Networks Based on Fractional-Order Hyperbolic PDEs with Delayed Coupling and Space-Varying Coefficients
by Chengyan Yang, Jin Wang, Muwei Jian and Jiashu Dai
Fractal Fract. 2024, 8(9), 525; https://doi.org/10.3390/fractalfract8090525 - 9 Sep 2024
Viewed by 526
Abstract
This paper studies synchronization behaviors of two sorts of non-linear fractional-order complex spatio-temporal networks modeled by hyperbolic space-varying PDEs (FCSNHSPDEs), respectively, with time-invariant delays and time-varying delays, including one delayed coupling. One distributed controller with space-varying control gains is firstly designed. For time-invariant [...] Read more.
This paper studies synchronization behaviors of two sorts of non-linear fractional-order complex spatio-temporal networks modeled by hyperbolic space-varying PDEs (FCSNHSPDEs), respectively, with time-invariant delays and time-varying delays, including one delayed coupling. One distributed controller with space-varying control gains is firstly designed. For time-invariant delayed cases, sufficient conditions for synchronization of FCSNHSPDEs are presented via LMIs, which have no relation to time delays. For time-varying delayed cases, synchronization conditions of FCSNHSPDEs are presented via spatial algebraic LMIs (SALMIs), which are related to time delay varying speeds. Finally, two examples show the validity of the control approaches. Full article
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16 pages, 1446 KiB  
Article
Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy
by Jiawei Wu, Yongguang Yu and Guojian Ren
Fractal Fract. 2024, 8(5), 246; https://doi.org/10.3390/fractalfract8050246 - 23 Apr 2024
Cited by 1 | Viewed by 1096
Abstract
Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for [...] Read more.
Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results. Full article
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19 pages, 655 KiB  
Article
Fixed-Time Synchronization for Fractional-Order Cellular Inertial Fuzzy Neural Networks with Mixed Time-Varying Delays
by Yeguo Sun, Yihong Liu and Lei Liu
Fractal Fract. 2024, 8(2), 97; https://doi.org/10.3390/fractalfract8020097 - 4 Feb 2024
Cited by 1 | Viewed by 1481
Abstract
Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category [...] Read more.
Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category of fractional-order cellular-inertial fuzzy neural networks (FCIFNNs) that involve mixed time-varying delays (MTDs), including both discrete and distributed delays. Firstly, we establish an appropriate transformation variable to reformulate FCIFNNs with MTD into a differential first-order system. Then, utilizing the finite-time stability (FETS) theory and Lyapunov functionals (LFs), we establish some new effective criteria for achieving FDTS of the response system (RS) and drive system (DS). Eventually, we offer two numerical examples to display the effectiveness of our proposed synchronization strategies. Moreover, we also demonstrate the benefits of our approach through an application in image encryption. Full article
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19 pages, 1201 KiB  
Article
Adaptive Output Synchronization of Coupled Fractional-Order Memristive Reaction-Diffusion Neural Networks
by Feng You, Hong-An Tang, Yanhong Wang, Zi-Yi Xia and Jin-Wei Li
Fractal Fract. 2024, 8(2), 78; https://doi.org/10.3390/fractalfract8020078 - 25 Jan 2024
Cited by 2 | Viewed by 1304
Abstract
This article discusses the adaptive output synchronization problem of coupled fractional-order memristive reaction-diffusion neural networks (CFOMRDNNs) with multiple output couplings or multiple output derivative couplings. Firstly, by using Lyapunov functional and inequality techniques, an adaptive output synchronization criterion for CFOMRDNNs with multiple output [...] Read more.
This article discusses the adaptive output synchronization problem of coupled fractional-order memristive reaction-diffusion neural networks (CFOMRDNNs) with multiple output couplings or multiple output derivative couplings. Firstly, by using Lyapunov functional and inequality techniques, an adaptive output synchronization criterion for CFOMRDNNs with multiple output couplings is proposed. Then, an adaptive controller is designed for ensuring the output synchronization of CFOMRDNNs with multiple output derivative couplings. Finally, two numerical examples are given to verify the effectiveness of the theoretical results. Full article
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