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Leader-following consensus of nonlinear fractional-order multi-agent systems over directed networks

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Abstract

This paper investigates the leader-following consensus of nonlinear fractional-order multi-agent systems where the linear part is depicted by the general linear dynamics on directed networks with the order p belonging to \(p \in (0,1]\) and \(p \in (1,2)\), respectively. By utilizing the Mittag-Leffler function, the Laplace transform, and the inequality technique, some algebraic-type consensus tracking criteria relying on the coupling strength, the coupling gain matrix and the network structure are obtained. It is interesting to find that the leader-following consensus can be attained by only using the position information among the agent and its neighbors for \(p \in (0,1]\) and \(p \in (1,2)\). The theoretical results are illustrated by several numerical simulation examples.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61873318 and 61473129, the Natural Science Foundation of Hubei Province of China under Grant No. 2018CFA058, the Wuhan Morning Light Plan of Youth Science and Technology under Grant No. 2017050304010288, the Fundamental Research Funds for the Central Universities [Grant Number HUST: 2017KFYXJJ178], and the Program for HUST Academic Frontier Youth Team.

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  1. School of Artificial Intelligence and Automation, Image Processing and Intelligent Control Key Laboratory of Education Ministry of China, Huazhong University of Science and Technology, Luoyu Road 1037, Wuhan, 430074, China

    Yanyan Ye & Housheng Su

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  1. Yanyan Ye
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  2. Housheng Su
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Correspondence to Housheng Su.

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Ye, Y., Su, H. Leader-following consensus of nonlinear fractional-order multi-agent systems over directed networks. Nonlinear Dyn 96, 1391–1403 (2019). https://doi.org/10.1007/s11071-019-04861-6

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