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Fractal Fract
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Advances in Fractional-Order Multiagent Systems: Theory and Applications
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Advances in Fractional-Order Multiagent Systems: Theory and Applications

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

Deadline for manuscript submissions: 25 August 2024 | Viewed by 6595

Special Issue Editor

Dr. Ping Gong

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, China
Interests: fractional-order equations and systems; distributed optimization and control of multi-agent systems

Special Issue Information

Dear Colleagues,

Multi-agent systems involve a group of agents that perceive and act to complete a complex task in a distributed manner. As a generalization of integer‒order multiagent systems, fractional-order multiagent systems possess significant advantages in accurately modeling and characterizing dynamic behaviors of many real-world systems because of their unique characteristics of historical memory. There has been a growing number of works about fractional-order multiagent systems in recent years, e.g., distributed coordination problems including consensus problems, tracking problems, containment problems, etc. Some real-world engineering systems can be found in the networks of mobile robots, unmanned aerial vehicles, and automated transportation, which are always corrupted by external disturbances, system uncertainties, sensor noises, and component faults/malfunctions. The study of fractional-order multi-agent systems with external disturbances, system uncertainties, sensor noises, and component faults/malfunctions has significant importance in both theory and practice. We welcome both theoretical advances and potential applications for distributed coordination control and optimization of fractional-order multiagent systems.

The focus of this Special Issue is to continue to advance research in all aspects of fractional-order multiagent systems, including the theory, design, implementation, and application of fractional-order multiagent systems. Topics that are invited for submission include (but are not limited to):

  • Linear fractional-order multi-agent systems;
  • Nonlinear fractional-order multi-agent systems;
  • Uncertain fractional-order multi-agent systems;
  • Distributed coordination of fractional-order multi-agent systems;
  • Distributed optimization of fractional-order multi-agent systems;
  • Convergence time analysis of fractional-order multi-agent systems;
  • Adaptive/robust control of fractional-order multi-agent systems;
  • Fault-tolerant control of fractional-order multi-agent systems;
  • Applications of fractional-order multi-agent systems.

Dr. Ping Gong
Guest Editor

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

  • fractional-order dynamics
  • multiagent systems
  • distributed coordination control
  • nonlinear control
  • stability analysis
  • algorithm design

Published Papers (6 papers)

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Research

19 pages, 435 KiB  
Article
Impulsive Control of Variable Fractional-Order Multi-Agent Systems
by Ravi P. Agarwal, Snezhana Hristova and Donal O’Regan
Fractal Fract. 2024, 8(5), 259; https://doi.org/10.3390/fractalfract8050259 - 26 Apr 2024
Viewed by 262
Abstract
The main goal of the paper is to present and study models of multi-agent systems for which the dynamics of the agents are described by a Caputo fractional derivative of variable order and a kernel that depends on an increasing function. Also, the [...] Read more.
The main goal of the paper is to present and study models of multi-agent systems for which the dynamics of the agents are described by a Caputo fractional derivative of variable order and a kernel that depends on an increasing function. Also, the order of the fractional derivative changes at update times. We study a case for which the exchanged information between agents occurs only at initially given update times. Two types of linear variable-order Caputo fractional models are studied. We consider both multi-agent systems without a leader and multi-agent systems with a leader. In the case of multi-agent systems without a leader, two types of models are studied. The main difference between the models is the fractional derivative describing the dynamics of agents. In the first one, a Caputo fractional derivative with respect to another function and with a continuous variable order is applied. In the second one, the applied fractional derivative changes its constant order at each update time. Mittag–Leffler stability via impulsive control is defined, and sufficient conditions are obtained. In the case of the presence of a leader in the multi-agent system, the dynamic of the agents is described by a Caputo fractional derivative with respect to an increasing function and with a constant order that changes at each update time. The leader-following consensus via impulsive control is defined, and sufficient conditions are derived. The theoretical results are illustrated with examples. We show with an example the leader’s influence on the consensus. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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19 pages, 1200 KiB  
Article
Quantization-Based Event-Triggered H∞ Consensus for Discrete-Time Markov Jump Fractional-Order Multiagent Systems with DoS Attacks
by Yi Lu, Xiru Wu, Yaonan Wang, Lihong Huang and Qingjin Wei
Fractal Fract. 2024, 8(3), 147; https://doi.org/10.3390/fractalfract8030147 - 02 Mar 2024
Viewed by 969
Abstract
This paper investigates the H∞ consensus problem of discrete-time Markov jump fractional-order multiagent systems (DTMJFOMASs) under denial-of-service (DoS) attacks. By applying the short-memory principle, we can obtain discrete-time Markov jump multiagent systems with partially unknown probabilities. A novel quantized event-triggering mechanism (QETM), [...] Read more.
This paper investigates the H∞ consensus problem of discrete-time Markov jump fractional-order multiagent systems (DTMJFOMASs) under denial-of-service (DoS) attacks. By applying the short-memory principle, we can obtain discrete-time Markov jump multiagent systems with partially unknown probabilities. A novel quantized event-triggering mechanism (QETM), based on a mode-dependent logarithmic quantizer, is proposed to enhance transmission efficiency among multiagents. A distributed controller with quantized output is developed. Sufficient conditions are provided to ensure the system achieves H∞ consensus through Lyapunov stability theory. Finally, two examples are given to verify the effectiveness of the proposed model. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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12 pages, 20398 KiB  
Article
A Discrete-Time Fractional-Order Flocking Control Algorithm of Multi-Agent Systems
by Haotian Chen, Ming He, Wei Han, Sicong Liu and Chenyue Wei
Fractal Fract. 2024, 8(2), 85; https://doi.org/10.3390/fractalfract8020085 - 27 Jan 2024
Viewed by 1063
Abstract
In this paper, a discrete-time fractional flocking control algorithm of multi-agent systems is put forward to address the slow convergence issue of multi-agent systems. Firstly, by introducing Grünwald-Letnikov (G-L) fractional derivatives, the algorithm allows agents to utilize historical information when updating their states. [...] Read more.
In this paper, a discrete-time fractional flocking control algorithm of multi-agent systems is put forward to address the slow convergence issue of multi-agent systems. Firstly, by introducing Grünwald-Letnikov (G-L) fractional derivatives, the algorithm allows agents to utilize historical information when updating their states. Secondly, based on the Lyapunov stability theory, the convergence of the algorithm is proven. Finally, simulations are conducted to verify the effectiveness of the proposed algorithm. Comparisons are made between the proposed algorithm and other methods. The results show that the proposed algorithm can effectively improve the convergence speed of multi-agent systems. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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20 pages, 2332 KiB  
Article
Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults
by Ke Sun, Zhiyao Ma, Guowei Dong and Ping Gong
Fractal Fract. 2023, 7(12), 862; https://doi.org/10.3390/fractalfract7120862 - 04 Dec 2023
Viewed by 1133
Abstract
In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface [...] Read more.
In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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21 pages, 2498 KiB  
Article
Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs
by Kun Wang, Ping Gong and Zhiyao Ma
Fractal Fract. 2023, 7(11), 813; https://doi.org/10.3390/fractalfract7110813 - 09 Nov 2023
Cited by 2 | Viewed by 1051
Abstract
This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global [...] Read more.
This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time T0. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time T1, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time T2, and afterwards minimize the convex time-varying global cost function within a fixed time T3. The upper bound of each fixed time Tm(m=0,1,2,3) is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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27 pages, 6978 KiB  
Article
Distributed Adaptive Optimization Algorithm for Fractional High-Order Multiagent Systems Based on Event-Triggered Strategy and Input Quantization
by Xiaole Yang, Jiaxin Yuan, Tao Chen and Hui Yang
Fractal Fract. 2023, 7(10), 749; https://doi.org/10.3390/fractalfract7100749 - 11 Oct 2023
Cited by 3 | Viewed by 1069
Abstract
This paper investigates the distributed optimization problem (DOP) for fractional high-order nonstrict-feedback multiagent systems (MASs) where each agent is multiple-input–multiple-output (MIMO) dynamic and contains uncertain dynamics. Based on the penalty-function method, the consensus constraint is eliminated and the global objective function is reconstructed. [...] Read more.
This paper investigates the distributed optimization problem (DOP) for fractional high-order nonstrict-feedback multiagent systems (MASs) where each agent is multiple-input–multiple-output (MIMO) dynamic and contains uncertain dynamics. Based on the penalty-function method, the consensus constraint is eliminated and the global objective function is reconstructed. Different from the existing literatures, where the DOPs are addressed for linear MASs, this paper deals with the DOP through using radial basis function neural networks (RBFNNs) to approximate the unknown nonlinear functions for high-order MASs. To reduce transmitting and computational costs, event-triggered scheme and quantized control technology are combined to propose an adaptive backstepping neural network (NN) control protocol. By applying the Lyapunov stability theory, the optimal consensus error is proved to be bounded and all signals remain semi-global uniformly ultimately bounded. Simulation shows that all agents reach consensus and errors between agents’ outputs and the optimal solution is close to zero with low computational costs. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)
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