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Chin. Phys. B, 2021, Vol. 30(7): 070701    DOI: 10.1088/1674-1056/abe113
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Consensus problems on networks with free protocol

Xiaodong Liu(柳晓东)1 and Lipo Mo(莫立坡)1,2,†
1 School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China;
2 Key Laboratory of Power Big Data of Guizhou Province, Guizhou Institute of Technology, Guiyang 550003, China
Abstract  In the real world, rule makers can only restrict, not completely control the behavior of the governed, while the governed can only choose their behavior patterns under these restrictions. In this paper, we design a new control protocol called free protocol to describe this situation. First, we calculate consensus probabilities based on the information of the interaction networks. Then, sufficient conditions are obtained for all agents converging to a same value with probability one. Finally, numerical simulation results are given to verify the above results.
Keywords:  multi-agent systems      random protocol      consensus with probability one  
Received:  01 December 2020      Revised:  09 January 2021      Accepted manuscript online:  29 January 2021
PACS:  07.05.Dz (Control systems)  
  05.10.-a (Computational methods in statistical physics and nonlinear dynamics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61973329) and the Beijing Natural Science Foundation, China (Grant No. Z180005).
Corresponding Authors:  Lipo Mo     E-mail:

Cite this article: 

Xiaodong Liu(柳晓东) and Lipo Mo(莫立坡) Consensus problems on networks with free protocol 2021 Chin. Phys. B 30 070701

[1] Shi J, Yue D and Weng S X 2018 Trans. Institute of Measurement and Control 41 1553
[2] Bidram A, Davoudi A and Lewis F L 2013 IEEE Trans. Power Systems 28 3462
[3] Dong X W, Yu B C, Shi Z Y and Zhong Y S 2015 IEEE Trans. Control Systems Technol. 23 340
[4] Dong X W, Zhou Y, Ren Z and Zhong Y S 2016 Control Engineering Practice 46 26
[5] Atzeni I, Ordonez L G, Scutari G, Palomar D P and Fonollosa J R 2013 IEEE Trans. Smart Grid 4 866
[6] Gao H Y, Hu A H, Shen W Q and Jiang Z X 2019 Chin. Phys. B 28 060501
[7] Shahamatkhah E and Tabatabaei M 2018 Chin. Phys. B 27 010701
[8] Wang J H, Xu Y L, Zhang J and Yang D D 2018 Chin. Phys. B 27 040504
[9] Chen X, Yin L Y, Liu Y T and Liu H 2019 Chin. Phys. B 28 090701
[10] Mo L P, Guo S Y and Yu Y G 2018 Chin. Phys. B 27 070504
[11] Zhao L, Yu J P, Yu H S and Lin C 2019 Int. J. Robust and Nonlinear Control 29 2742
[12] Mo L P and Guo S Y 2019 J. Systems Sci. Complexity 32 835
[13] Zhang Y L, Wen G G, Peng Z X, Yu Y G and Rahmani A 2018 Trans. Institute of Measurement and Control 41 1313
[14] Han G S, Guan Z H, Li J, He D X and Zheng D F 2016 Nonlinear Dynamics 84 1771
[15] Fan M C, Zhang H T and Wang M M 2014 Commun. Nonlin. Sci. Numer. Simular. 19 3313
[16] Altafini C 2012 IEEE Trans. Automatic Control 58 935
[17] Hu J P and Zheng W X 2014 52nd IEEE Conference on Decision and Control, December 10-13, 2013, Florence, Italy, p. 3451
[18] Guo X, Liang J L and Lu J Q 2019 Int. J. Control Automation and Systems 17 1041
[19] Zheng H W and Chen J 2019 Int. J. Robust and Nonlinear Control 27 3
[20] He G, Liu J, Wu Y L and Fang J A 2020 Int. J. Control Automation and Systems 18 303
[21] Ma C Q and Qin Z Y 2016 IET Control Theory and Applications 10 2306
[22] Pan L L, Shao H B, Mesbahi M, Xi Y G and Li D W 2018 IEEE Trans. Circuits and Systems Ⅱ-Express Briefs 66 1441
[23] Wu Y Z, Zhao Y Y and Hu J P 2019 IEEE Trans. Systems Man Cybernetics-Systems 49 2189
[24] Ma C Q and Xie L H 20 IEEE Trans. Systems Man Cybernetics-Systems 50 1976
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