Fractal and Fractional

Research

16 pages, 2999 KiB

Open AccessArticle

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

by Jing Li, Zixiang Yan, Xingyun Shi and Xuqiong Luo

Fractal Fract. 2024, 8(10), 563; https://doi.org/10.3390/fractalfract8100563 - 28 Sep 2024

Cited by 1 | Viewed by 615

Abstract

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the [...] Read more.

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions. Full article

(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 1994 KiB

Open AccessArticle

Iterative Learning Formation Control via Input Sharing for Fractional-Order Singular Multi-Agent Systems with Local Lipschitz Nonlinearity

by Guangxu Wang, Rui Wang, Danhu Yi, Xingyu Zhou and Shuyu Zhang

Fractal Fract. 2024, 8(6), 347; https://doi.org/10.3390/fractalfract8060347 - 11 Jun 2024

Viewed by 887

Abstract

For a class of fractional-order singular multi-agent systems (FOSMASs) with local Lipschitz nonlinearity, this paper proposes a closed-loop

D^{α}

-type iterative learning formation control law via input sharing to achieve the stable formation of FOSMASs in a finite time. Firstly, the formation [...] Read more.

For a class of fractional-order singular multi-agent systems (FOSMASs) with local Lipschitz nonlinearity, this paper proposes a closed-loop

D^{α}

-type iterative learning formation control law via input sharing to achieve the stable formation of FOSMASs in a finite time. Firstly, the formation control issue of FOSMASs with local Lipschitz nonlinearity under the fixed communication topology (FCT) is transformed into the consensus tracking control scenario. Secondly, by virtue of utilizing the characteristics of fractional calculus and the generalized Gronwall inequality, sufficient conditions for the convergence of formation error are given. Then, drawing upon the FCT, the iteration-varying switching communication topology is considered and examined. Ultimately, the validity of the

D^{α}

-type learning method is showcased through two numerical cases. Full article

(This article belongs to the Special Issue Advances in Fractional-Order Multiagent Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 435 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 1067

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)

► Show Figures

Figure 1

19 pages, 1200 KiB

Open AccessArticle

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 - 2 Mar 2024

Cited by 1 | Viewed by 1412

Abstract

This paper investigates the

H_{\infty}

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_{\infty}

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_{\infty}

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)

► Show Figures

Figure 1

12 pages, 20398 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 1461

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)

► Show Figures

Figure 1

20 pages, 2332 KiB

Open AccessArticle

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 - 4 Dec 2023

Viewed by 1588

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)

► Show Figures

Figure 1

21 pages, 2498 KiB

Open AccessArticle

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 - 9 Nov 2023

Cited by 4 | Viewed by 1482

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

T_{0}

. 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

T_{1}

, 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

T_{2}

, and afterwards minimize the convex time-varying global cost function within a fixed time

T_{3}

. The upper bound of each fixed time

T_{m} (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)

► Show Figures

Figure 1

27 pages, 6978 KiB

Open AccessArticle

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 5 | Viewed by 1478

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)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Advances in Fractional-Order Multiagent Systems: Theory and Applications

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI