# American Institute of Mathematical Sciences

September  2017, 7(3): 345-357. doi: 10.3934/naco.2017022

## A type of new consensus protocol for two-dimension multi-agent systems

 Institute of Automation, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China

* Corresponding author: Zhang Yibo

The reviewing process of the paper was handled by Nanjing Huang as Guest Editors

Received  January 2016 Revised  June 2017 Published  July 2017

Fund Project: This work is supported by the National Natural Science Foundation of China (No. 61374083,61473264), Zhejiang Province Key Project of Science and Technology(No. 2014C03027), and Zhejiang Provincial Natural Science Foundation of China (No. LZ17F030002, LY17F030024).

A type of new consensus protocol for a two-dimension multi-agent system (MAS) is proposed. By introducing the conventional MAS and protocol, a dynamic equation of the first-order two-dimension MAS is proposed. then a new protocol with its Laplacian matrix is adopted. According to two types possible roots of character equations, two lemmas are proposed to show consensus asymptotical conditions. Furthermore, the convergence conditions of parameters are analyzed. Several simulated examples illustrate that consensus is achieved if the convergence conditions are satisfied.

Citation: Yibo Zhang, Jinfeng Gao, Jia Ren, Huijiao Wang. A type of new consensus protocol for two-dimension multi-agent systems. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 345-357. doi: 10.3934/naco.2017022
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##### References:
 [1] Y. Y. Chen and Y. P. Tian, Directed coordinated control for multi-agent formation motion onaset of given curves, Acta Automatica Sinica, 35 (2009), 1541-1549.  doi: 10.3724/SP.J.1004.2009.01541.  Google Scholar [2] H. Huang, C. B. Yu and Q. H. Wu, Autonomous scale control of multi-agent formations with only shape constraints, International Journal of Robust and Nonlinear Control, 23 (2013), 765-791.  doi: 10.1002/rnc.2800.  Google Scholar [3] A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, Proceedings of the 41st IEEE Conference on Decision and Control,, 48 (2003), 2953-2958.  doi: 10.1109/CDC.2003.812781.  Google Scholar [4] Z. K. Li, X. D. Liu, W. Ren and L. H. Xie, Distributed tracking control for linear multi-agent systems with a leader of bounded unknown input, IEEE Transactions on Automatic Control, 58 (2013), 518-523.  doi: 10.1109/TAC.2012.2208295.  Google Scholar [5] Z. Y. Lin, L. L. Wang, Z. M. Han and M. Y. Fu, Distributed formation control of multi-Agent systems using complex Laplacian, IEEE Transactions on Automatic Control, 59 (2014), 1765-1777.  doi: 10.1109/TAC.2014.2309031.  Google Scholar [6] C. Q. Ma and J. F. Zhang, Necessary and sufficient conditions for consensus ability of linear multi-agent systems, IEEE Transactions on Automatic Control, 55 (2010), 1263-1268.  doi: 10.1109/TAC.2010.2042764.  Google Scholar [7] W. Ren and E. Atkins, Distributed multi-vehicle coordinated control via local information exchange, International Journal of Robust and Nonlinear Control, 17 (2007), 1002-1033.  doi: 10.1002/rnc.1147.  Google Scholar [8] W. Yu and Y. F. Zheng, Dynamic behavior of multi-agent systems with distributed sampled control, Acta Automatica Sinica, 38 (2012), 357-365.  doi: 10.3724/SP.J.1004.2012.00357.  Google Scholar
All possible of multiple results of $\bar{\mu} _{i\pm }$
Simulation results 1 of condition (1) in Lemma 1
Simulation results 2 of condition (1) in Lemma 1
Simulation results 1 of condition (2) in Lemma 1
Simulation results 2 of condition (2) in Lemma 1
Simulation results 2 of condition (3) in Lemma 1
Simulation results of condition (3) in Lemma 1
Simulation results of condition (3) in Lemma 1
Simulation results 1 of condition (1) in Lemma 2
Simulation results 2 of condition (1) in Lemma 2
Simulation results 1 of condition (2) in Lemma 2
Simulation results 1 of condition (2) in Lemma 2
Simulation results if Lemma 1 is not hold
Simulation results if Lemma 2 is not hold
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