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Fractal Fract
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Fractional Dynamics and Control in Multi-Agent Systems and Networks
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Fractional Dynamics and Control in Multi-Agent Systems and Networks

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

Deadline for manuscript submissions: 20 May 2026 | Viewed by 5187

Special Issue Editors

Prof. Dr. Huaiqin Wu

E-Mail Website
Guest Editor
School of Science, Yanshan University, Qinhuangdao 066001, China
Interests: complex networks; neural networks; multi-agent systems
Prof. Dr. Cheng Hu

E-Mail Website
Guest Editor
College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Interests: nonlinear complex systems; fractional-order system theory and application; neural networks dynamics and control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As an extension of integer order calculus, fractional-order calculus has good advantages in memory and genetic properties. Therefore, it can be used to model complex systems, like multi-agent systems (MASs) and complex networks (CNs),  and can also represent the dynamic behavior of complex real-world phenomena more accurately. MASs and CNs have many potential applications, as with, for example,  satellite formation, distributed optimization, multi-robot collaboration, traffic networks, and information science, amongst others. Thus, in recent years, more and more scholars have focused on studying the dynamic behavior and control problems of fractional-order MASs or CNs, such as consensus, path-tracking, and attitude control issues of MASs, and the synchronization, topology identification, and passivity issues of CNs. However, in engineering applications, these systems are often subject to the effects of malicious attacks, external interference, or actuator failures. Therefore, further research on fractional-order MASs and CNs in various complex external environments is of both theoretical and practical significance.

The focus of this Special Issue is to advance research on topics relating to modeling, dynamic analysis, and the control and application of fractional-order MASs or CNs, including their theory, design, implementation, and application. Topics that are invited for submission include (but are not limited to) the following:

  • Theory and implementation of fractional-order MASs and CNs;
  • Dynamics analysis of fractional-order MASs and CNs;
  • Distributed cooperative control of fractional-order MASs and CNs;
  • Distributed optimization of fractional-order MASs and CNs;
  • Secure consensus or synchronization of fractional-order MASs or CNs under cyber attacks;
  • Applications of fractional-order MASs and CNs.

Prof. Dr. Huaiqin Wu
Prof. Dr. Cheng Hu
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 250 words) can be sent to the Editorial Office for assessment.

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

  • system model
  • fractional-order dynamics
  • MASs and CNs
  • stability analysis
  • nonlinear control

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Published Papers (7 papers)

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Research

26 pages, 7148 KB  
Article
Synchronization and Identification in Finite Time for Fractional Multi-Delayed Complex Networks with Hybrid Couplings
by Lifei Wang and Huaiqin Wu
Fractal Fract. 2026, 10(4), 241; https://doi.org/10.3390/fractalfract10040241 - 3 Apr 2026
Viewed by 316
Abstract
This paper investigates the finite time stability (FTS) of multi-delayed systems with Riemann-Liouville fractional order (RLFO). Firstly, a lemma on the FTS criterion is established for RLFO multi-delay systems, which lays the theoretical groundwork for the subsequent analysis of network synchronization and identification. [...] Read more.
This paper investigates the finite time stability (FTS) of multi-delayed systems with Riemann-Liouville fractional order (RLFO). Firstly, a lemma on the FTS criterion is established for RLFO multi-delay systems, which lays the theoretical groundwork for the subsequent analysis of network synchronization and identification. Secondly, for hybrid coupled complex networks (CNs) with RLFO, multiple delays, and a non-Lipschitz vector field, we explore finite-time synchronization and topology identification (TI) without imposing the linear independence condition (LIC). This is achieved by constructing: (1) a regulated control network with topology observers, and (2) an auxiliary network with isolated nodes. Based on the proposed FTS criterion, along with the designed control protocol and adaptive topology observer, sufficient conditions for the finite time synchronization and TI of multi-delayed CNs are derived as linear matrix inequalities (LMIs). Finally, a numerical simulation on the Lorenz system is carried out to validate the derived results and evaluate the efficacy of the proposed method. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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21 pages, 1110 KB  
Article
Fully Distributed Observer-Based Dynamic Double-Event-Triggered Bipartite Consensus Tracking of Fractional-Order Multi-Agent Systems with Input Saturation
by Xiaohe Li, Jing Bai, Yijia Sun and Guoguang Wen
Fractal Fract. 2026, 10(3), 162; https://doi.org/10.3390/fractalfract10030162 - 28 Feb 2026
Viewed by 328
Abstract
This paper investigates the fully distributed observer-based dynamic double-event-triggered bipartite consensus tracking problem of fractional-order multi-agent systems (FOMASs) with input saturation under a directed graph. First, to address this complex challenge, a pull-based dynamic double-event-triggered mechanism (DDETM) with different event-triggered conditions and capable [...] Read more.
This paper investigates the fully distributed observer-based dynamic double-event-triggered bipartite consensus tracking problem of fractional-order multi-agent systems (FOMASs) with input saturation under a directed graph. First, to address this complex challenge, a pull-based dynamic double-event-triggered mechanism (DDETM) with different event-triggered conditions and capable of operating independently is designed, which can effectively reduce communication costs and controller updates concurrently. Then, the low-gain feedback technique is used to solve the input saturation problem faced by FOMASs under a directed graph. Based on the estimated state information, a fully distributed control protocol with pull-based DDETM is proposed to ensure the achievement of bipartite consensus tracking for FOMASs. A noteworthy feature of this control protocol is its ability to achieve system stability without the need for global information. Correspondingly, the sufficient conditions for achieving bipartite consensus is obtained with the help of low gain feedback technology and Lyapunov stability theory. Moreover, the Zeno behavior is precluded. Finally, a simulation example is presented to illustrate the theoretical results. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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30 pages, 5422 KB  
Article
Iterative Learning Bipartite Consensus Control for Fractional-Order Switched Nonlinear Heterogeneous MASs with Cooperative and Antagonistic Interactions
by Song Yang and Siyuan Chen
Fractal Fract. 2026, 10(2), 98; https://doi.org/10.3390/fractalfract10020098 - 2 Feb 2026
Viewed by 569
Abstract
The coordination of switched fractional-order nonlinear heterogeneous multi-agent systems (FONHMASs) with cooperative and antagonistic interactions presents significant challenges due to the complex coupling of switched fractional-order dynamics. Crucially, existing control methods typically rely on integer-order assumptions and precise system modeling, which are inadequate [...] Read more.
The coordination of switched fractional-order nonlinear heterogeneous multi-agent systems (FONHMASs) with cooperative and antagonistic interactions presents significant challenges due to the complex coupling of switched fractional-order dynamics. Crucially, existing control methods typically rely on integer-order assumptions and precise system modeling, which are inadequate for capturing the inherent non-local memory behaviors of fractional dynamics. Furthermore, they generally assume fixed agent dynamics, and cannot be applied to switched FONHMASs where the continuity of agents’ dynamics is violated at switching instants. Considering the constraints of precise modeling difficulties and limited task time for switched FONHMASs in practice, a distributed Dα-type iterative learning control (ILC) protocol is proposed to achieve bipartite consensus in the presence of cooperative and antagonistic interactions. Also, without relying on repetitive initial conditions, based on a presented initial state learning mechanism and Dα-type ILC protocol, the bipartite consensus error convergence property with each iteration is achieved. Additionally, in consideration of external disturbances, the robustness of the iterative bipartite consensus controller for the switched FONHMASs is analyzed. Simulation results confirm that the switched FONHMASs achieve the convergence and robustness of the bipartite consensus errors along the iteration direction. In addition, the proposed Dα-type ILC protocol achieves a maximum root-mean-square-error (MRMSE) of 0.0168 in time domain, significantly outperforming the integer-order ILC (MRMSE = 0.3601) and fractional-order PID control (MRMSE = 0.7550), confirming its superiority. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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29 pages, 6260 KB  
Article
Multi-Objective Optimization and Load-Flow Analysis in Complex Power Distribution Networks
by Tariq Ali, Muhammad Ayaz, Husam S. Samkari, Mohammad Hijji, Mohammed F. Allehyani and El-Hadi M. Aggoune
Fractal Fract. 2026, 10(2), 82; https://doi.org/10.3390/fractalfract10020082 - 25 Jan 2026
Viewed by 612
Abstract
Modern power distribution networks are increasingly challenged with nonlinear operating conditions, the high penetration of distributed energy resources, and conflicting operational objectives such as loss minimization and voltage regulation. Existing load-flow optimization approaches often suffer from slow convergence, premature stagnation in non-convex search [...] Read more.
Modern power distribution networks are increasingly challenged with nonlinear operating conditions, the high penetration of distributed energy resources, and conflicting operational objectives such as loss minimization and voltage regulation. Existing load-flow optimization approaches often suffer from slow convergence, premature stagnation in non-convex search spaces, and limited robustness when handling conflicting multi-objective performance criteria under fixed network constraints. To address these challenges, this paper proposes a Fractional Multi-Objective Load Flow Optimizer (FMOLFO), which integrates a fractional-order numerical regularization mechanism with an adaptive Pareto-based Differential Evolution framework. The fractional-order formulation employed in FMOLFO operates over an auxiliary iteration domain and serves as a numerical regularization strategy to improve the sensitivity conditioning and convergence stability of the load-flow solution, rather than modeling the physical time dynamics or memory effects of the power system. The optimization framework simultaneously minimizes physically consistent active power loss and voltage deviation within existing network operating constraints. Extensive simulations on IEEE 33-bus and 69-bus benchmark distribution systems demonstrate that FMOLFO achieves an up to 27% reduction in active power loss, improved voltage profile uniformity, and faster convergence compared with classical Newton–Raphson and metaheuristic baselines evaluated under identical conditions. The proposed framework is intended as a numerically enhanced, optimization-driven load-flow analysis tool, rather than a control- or dispatch-oriented optimal power flow formulation. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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30 pages, 2823 KB  
Article
A Fractional Calculus-Enhanced Multi-Objective AVOA for Dynamic Edge-Server Allocation in Mobile Edge Computing
by Aadel Mohammed Alatwi, Bakht Muhammad Khan, Abdul Wadood, Shahbaz Khan, Hazem M. El-Hageen and Mohamed A. Mead
Fractal Fract. 2026, 10(1), 28; https://doi.org/10.3390/fractalfract10010028 - 4 Jan 2026
Cited by 1 | Viewed by 429
Abstract
Dynamic edge-server allocation in mobile edge computing (MEC) networks is a challenging multi-objective optimization problem due to highly dynamic user demands, spatiotemporal traffic variations, and the need to simultaneously minimize service latency and workload imbalance. Existing heuristic and metaheuristic-based approaches for this problem [...] Read more.
Dynamic edge-server allocation in mobile edge computing (MEC) networks is a challenging multi-objective optimization problem due to highly dynamic user demands, spatiotemporal traffic variations, and the need to simultaneously minimize service latency and workload imbalance. Existing heuristic and metaheuristic-based approaches for this problem often suffer from premature convergence, limited exploration–exploitation balance, and inadequate adaptability to dynamic network conditions, leading to suboptimal edge-server placement and inefficient resource utilization. Moreover, most existing methods lack memory-aware search mechanisms, which restrict their ability to capture long-term system dynamics. To address these limitations, this paper proposes a Fractional-Order Multi-Objective African Vulture Optimization Algorithm (FO-MO-AVOA) for dynamic edge-server allocation. By integrating fractional-order calculus into the standard multi-objective AVOA framework, the proposed method introduces long-memory effects that enhance convergence stability, search diversity, and adaptability to time-varying workloads. The performance of FO-MO-AVOA is evaluated using realistic MEC network scenarios and benchmarked against several well-established metaheuristic algorithms. Simulation outcomes reveal that FO-MO-AVOA achieves 40–46% lower latency, 38–45% reduction in workload imbalance, and up to 28–35% reduction in maximum workload compared to competing methods. Extensive experiments conducted on real-world telecom network data demonstrate that FO-MO-AVOA consistently outperforms state-of-the-art multi-objective optimization algorithms in terms of convergence behaviour, Pareto-front quality, and overall system performance. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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21 pages, 903 KB  
Article
Boundary Control for Consensus in Fractional-Order Multi-Agent Systems Under DoS Attacks and Actuator Failures
by Qiang Qi, Xiao Chen, Dejian Wang, Jiashu Dai, Yuqian Yang and Chengdong Yang
Fractal Fract. 2025, 9(11), 745; https://doi.org/10.3390/fractalfract9110745 - 18 Nov 2025
Viewed by 943
Abstract
This paper investigates the consensus problem in fractional-order multi-agent systems (FOMASs) under Denial of Service (DoS) attacks and actuator faults. A boundary control strategy is proposed, which reduces dependence on internal sensors and actuators by utilizing only the state information at the system [...] Read more.
This paper investigates the consensus problem in fractional-order multi-agent systems (FOMASs) under Denial of Service (DoS) attacks and actuator faults. A boundary control strategy is proposed, which reduces dependence on internal sensors and actuators by utilizing only the state information at the system boundaries, significantly lowering control costs. To address DoS attacks, a buffer mechanism is designed to store valid control signals during communication interruptions and apply them once communication is restored, thereby enhancing the system’s robustness and stability. Additionally, this study considers the impact of actuator performance fluctuations on control effectiveness and proposes corresponding adjustment strategies to ensure that the system maintains consensus and stability even in the presence of actuator failures or performance variations. Finally, the effectiveness of the proposed method is validated through numerical experiments. The results show that, even under DoS attacks and actuator faults, the system can still successfully achieve consensus and maintain good stability, demonstrating the feasibility and effectiveness of this control approach in complex environments. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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18 pages, 5095 KB  
Article
Discrete-Time Fractional-Order Sliding Mode Attitude Control of Multi-Spacecraft Systems Based on the Fully Actuated System Approach
by Yiqi Chen and Shuyi Shao
Fractal Fract. 2025, 9(7), 435; https://doi.org/10.3390/fractalfract9070435 - 1 Jul 2025
Cited by 1 | Viewed by 1117
Abstract
In practical applications, most systems operate based on digital signals obtained through sampling. Applying fractional-order control to spacecraft attitude control is meaningful for achieving better performance, especially in the coordination of the multi-spacecraft attitude system. In this paper, a discrete-time fractional-order sliding mode [...] Read more.
In practical applications, most systems operate based on digital signals obtained through sampling. Applying fractional-order control to spacecraft attitude control is meaningful for achieving better performance, especially in the coordination of the multi-spacecraft attitude system. In this paper, a discrete-time fractional-order sliding mode attitude control problem is studied for multi-spacecraft systems based on the fully actuated system approach. Firstly, a discrete-time disturbance observer based on the fractional-order theory is constructed to estimate the disturbance. Secondly, a discrete-time fractional-order sliding mode controller is designed by combining the transformed fully actuated discrete-time system and the disturbance observer. Subsequently, every spacecraft can track the desired attitude under the designed controller. Finally, the simulation results show that the developed control method achieves faster convergence, smaller overshoot, and higher control accuracy. Full article
(This article belongs to the Special Issue Fractional Dynamics and Control in Multi-Agent Systems and Networks)
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