Distributed coordination of fractional order multi-agent systems with communication delays

Abstract

Because of the complexity of the practical environments, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Under the connected network with directed weighted topologies, the dynamical characteristics of agents with fractional-order derivative operator is analyzed in this paper. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the distributed coordination of fractional-order multi-agent systems (FOMAS) with communication delays is studied, and a critical value of time delay is obtained to ensure the consensus of FOMAS. Since the integer-order model is a special case of fractional-order model, the extended results in this paper are in accordance with that of the integer-order model. Finally, numerical examples are provided to verify our results.MSC 2010 : Primary 34K37; Secondary 68T42, 93C85

Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control

“…Consensus of fractional-order multi-agent systems was first discussed by Cao, Li, Ren, and Chen (2010). Recently, more results about the consensus of fractional-order multi-agent systems have been published (Bai, Wen, Rahmania, & Yu, 2015;Bai, Wen, Rahmania, Yu, & Chu, 2016;Yang, Zhu, & Cao, 2014;Yu, Jiang, & Hu, 2015).…”

Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays

“…The distributed coordination of FOMAS with communication delays for continue-time and discrete-time systems were studied by Yang et.al. [6,7]. Motivated by the broad application of FOMAS, distributed containment control of FOMAS will be studied in this paper.…”

“…Recently, the problems of fractional calculus have been paid more and more attention since fractional operators have been broadly applied in more and more scientific *Corresponding Author: Hongyong Yang: School of Information and Electrical Engineering, Ludong University, Yantai 264025, China; Email: hyyang@yeah.net Fujun Han, Mei Zhao, Shuning Zhang, Jun Yue: School of Information and Electrical Engineering, Ludong University, Yantai 264025, China fields, for examples: in mechanics, physics, material science, informatics and engineering [1][2][3][4][5][6][7]. Not only can fractional order controllers be used to add robustness of control systems, but controlled more easily than that of integer-order systems [8,9].…”

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

“…In [19], a necessary and sufficient condition was derived to ensure the consensus of fractional-order systems with identical input delays over a directed topology. In [20,21], the authors successively studied the fractional-order system consensus control with communication delays, where homogeneous dynamics and heterogeneous dynamics were investigated. In [22], the consensus of linear and nonlinear fractional-order multiagent systems with input time delay was studied.…”