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Mathematical Problems in Engineering
Volume 2016, Article ID 1056594, 8 pages
Research Article

Necessary and Sufficient Conditions for Circle Formations of Mobile Agents with Coupling Delay via Sampled-Data Control

1School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing, Beijing 100083, China
2Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
3Intelligent Control Laboratory, College of Engineering, Peking University, Beijing 100871, China

Received 1 February 2016; Accepted 2 June 2016

Academic Editor: Weizhong Dai

Copyright © 2016 Jianwei Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A circle forming problem for a group of mobile agents governed by first-order system is investigated, where each agent can only sense the relative angular positions of its neighboring two agents with time delay and move on the one-dimensional space of a given circle. To solve this problem, a novel decentralized sampled-data control law is proposed. By combining algebraic graph theory with control theory, some necessary and sufficient conditions are established to guarantee that all the mobile agents form a pregiven circle formation asymptotically. Moreover, the ranges of the sampling period and the coupling delay are determined, respectively. Finally, the theoretical results are demonstrated by numerical simulations.