Consensus of multi-agent systems with distributed fractional order dynamics

Nava-Antonio, Guillermo; Fernández‐Anaya, Guillermo; Hernández‐Martínez, Eduardo Gamaliel; Jamous-Galante, J.; Ferreira, Enrique; Flores-Godoy, J.J.

doi:10.1109/iwcsn.2017.8276526

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…The Lyapunov direct method, used for analysis of stability, was first generalized for nonlinear time-varying DO systems in [ 355 , 356 , 357 ] and was used to determine the stability or asymptotic stability of certain nonlinear systems including a DO analog of the Lorenz system. The theoretical framework proposed in the studies [ 355 , 356 ] was then used to analyze different nonlinear time-varying DO systems including a DO consensus model [ 358 ], the DO Lorenz system [ 359 ], and the DO Van der Pol oscillator [ 330 , 360 ]. The consensus of multi-agent systems with fixed directed graphs and described by DODE, was analyzed in [ 358 ] and sufficient conditions were obtained for robust consensus in the presence and absence of external disturbances.…”

Section: Applications To Control Theorymentioning

confidence: 99%

“…The theoretical framework proposed in the studies [ 355 , 356 ] was then used to analyze different nonlinear time-varying DO systems including a DO consensus model [ 358 ], the DO Lorenz system [ 359 ], and the DO Van der Pol oscillator [ 330 , 360 ]. The consensus of multi-agent systems with fixed directed graphs and described by DODE, was analyzed in [ 358 ] and sufficient conditions were obtained for robust consensus in the presence and absence of external disturbances. Recently, the stability and control of a DO Van der Pol were analyzed in [ 330 ], wherein the intervals of the different model parameters at which this oscillator exhibits periodic, chaotic, and hyperchaotic behaviors, were calculated using Lyapunov exponents.…”

Section: Applications To Control Theorymentioning

confidence: 99%

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Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

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Section: Applications To Control Theorymentioning

confidence: 99%

Section: Applications To Control Theorymentioning

confidence: 99%

Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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“…Extensive introductory reviews of this topic can be found in W. Ren and Beard [21]; W. Ren and Cao [24]. Some of the ideas presented in those references have been generalized for fractional order systems, solely using the Caputo fractional derivative, for example: in Yu, Jiang, Hu, and Yu [25], an adaptive pinning control is used to realize leader-following consensus in a fractional multiagent system; Yin, Yue, and Hu [26] studied the consensus problem for fractional heterogeneous systems, made up of agents with different dynamics; Song, Cao, and Liu [27] proposed a distributed protocol to accomplish robust consensus, based on the information of second-order neighbors; Nava-Antonio et al [28] present sufficient conditions for consensus of multiagent systems with distributed fractional order; and G. Ren and Yu [29] gave conditions for fractional multiagent systems to achieve robust consensus, via Mittag-Leffler stability methods. That last article is the main inspiration of the second half of this paper, where we will extend the results of G. Ren and Yu [29] to be used in multiagent systems with five other fractional differentiation orders, with linear or nonlinear dynamics, and in the presence of external perturbations.…”

Section: Introductionmentioning

confidence: 99%

Consensus of Multiagent Systems Described by Various Noninteger Derivatives

et al. 2019

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In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems. These differ by being modeled with one of the following fractional derivatives: the Caputo derivative, the Caputo distributed order derivative, the variable order derivative, the conformable derivative, the local fractional derivative, or the distributed order conformable derivative (the latter defined in this work). Additionally, we apply these results to study the consensus of a fractional multiagent system, considering all of the aforementioned fractional operators. Our analysis covers multiagent systems with linear and nonlinear dynamics, affected by bounded external disturbances and described by fixed directed graphs. Lastly, examples, which are solved analytically and numerically, are presented to validate our contributions.

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An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order

Taghipour,

Shirzadi,

Safarpoor

2023

J Nonlinear Math Phys

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The subject of this paper is to propose a numerical algorithm for solving 2D diffusion and diffusion-wave equations of distributed order fractional derivatives. Such equations arise in modelling complex systems and have many important applications. Existence of integral term over the order of fractional derivative causes the high complexity of these equations and so their numerical solutions needs special cares. Using Gauss quadrature approach for discretizing the integral term of fractional derivative converts the distributed equation into a multi-term fractional differential equation. Then, the time variable is discretized with a suitable finite difference approach. The resultant semi-discretized equations are fully discretized by a radial basis function-generated finite difference based method. Convergence of the method are studied numerically. Various kind of test problems are considered for a comprehensive numerical study and the results confirm the efficiency of the method.

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Consensus of multi-agent systems with distributed fractional order dynamics

Cited by 3 publications

References 25 publications

Applications of Distributed-Order Fractional Operators: A Review

Applications of Distributed-Order Fractional Operators: A Review

Consensus of Multiagent Systems Described by Various Noninteger Derivatives

An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order

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