Abstract
Robust finite-time consensus problems in leader-following multi-agent directed networks with second-order nonlinear dynamics are considered in this paper. By using matrix theory, algebraic graph theory and finite-time control scheme, a class of continuous distributed control algorithms are designed in a quite unified way for each follower agent to reach consensus in a finite time. A numerical example is also employed to illustrate the effectiveness and correctness of our theoretical results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Trans. on Automatic Control, vol. 50, no. 5, pp. 655–661, May 2005.
W. Yu, G. Chen, M. Cao, and J. Kurths, “Secondorder consensus for multiagent systems with directed topologies and nonlinear dynamics,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 3, pp. 881–891, June 2010.
Q. Song, J. Cao, and W. Yu, “Second-order leaderfollowing consensus of nonlinear multi-agent systems via pinning control,” Syst. Control Lett., vol. 59, no. 9, pp. 553–562, September 2010.
W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, June 2010.
S. Khoo, L. Xie, and Z. Man, “Robust finite-time consensus tracking algorithm for multirobot systems,” IEEE Tran. Mechatronics, vol. 14, no. 2, pp. 219–228, April 2009.
W. Zhu and D. Cheng, “Leader-following consensus of second-order agents with multiple timevarying delays,” Automatica, vol. 46, no. 12, pp. 1994–1999, December 2010.
S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization,” vol. 38, no. 3, pp. 751–766, 2000.
M. P. Aghababa, S. Khanmohammadi, and G. Alizadeh, “Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 3080–3091, June 2011.
S. Yu, X. Yu, and Z. Man, “A fuzzy neural network approximator with fast terminal sliding mode and its applications,” Fuzzy Sets and Systems, vol. 148, no. 3, pp. 469–486, December 2004.
H. W. Wang and Q. K. Song, “State estimation for neural networks with mixed interval time-varying delays,” Neurocomputing, vol. 73, no. 7–9, pp. 1281–1288, March 2010.
X. He, C. D. Li, T. W. Huang, and C. J. Li, “Codimension two bifurcation in a delayed neural network with unidirectional coupling,” Nonlinear Analysis-Real World Applications, vol. 14, no. 2, pp. 1191–1202, April 2013.
S. P. Wen, Z. G. Zeng, and T. W. Huang, “H∞ filtering for neutral systems with mixed delays and multiplicative noises,” IEEE Trans. Circuits and Systems Part II, vol. 59, no. 11, pp. 820–824, 2012.
C. J. Li, C. D. Li, T. W. Huang, and X. F. Liao, “Impulsive effects on stability of high-order BAM neural networks with time delays,” Neurocomputing, vol. 74, no. 10, pp. 1541–1550, May 2011.
S. P. Wen, Z. G. Zeng, and T. W. Huang, “Adaptive synchronization of memristor-based Chua’s circuits,” Physics Letters A, vol. 376, no. 10, pp. 2775–2780, September 2012.
H. W. Wang and Q. K. Song, “Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays,” Neurocomputing, vol. 74, no. 10, pp. 1572–1584, May 2011.
S. P. Wen, Z. G. Zeng, and T. W. Huang, “Robust H∞ output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noises,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1061–1077, October 2012.
X. He, C. D. Li, and Y. L. Shu, “Bogdanov-Takens bifurcation in a single inertial neuron model with delay,” Neurocomputing, vol. 89, no. 15, pp. 193–201, July 2012.
S. P. Wen, Z. G. Zeng, and T. W. Huang, “Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays,” Neurocomputing, vol. 97, no. 15, pp. 233–240, November 2012.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editorial Board member Shengyuan Xu under the direction of Editor Hyungbo Shim.
Huaqing Li received his B.S. degree from Chongqing University of Posts and Telecommunications, Chongqing, China, in 2009. He received his Ph.D. degree in the College of Computer Science at Chongqing University, Chongqing, China, in 2013. His research interest focuses on nonlinear dynamical systems, bifurcation and chaos, neural networks and consensus of multi-agent systems.
Xiaofeng Liao received his B.S. and M.S. degrees in Mathematics from Sichuan University, Chengdu, China, in 1986 and 1992, respectively, and his Ph.D. degree in Circuits and Systems from the University of Electronic Science and Technology of China in 1997. From 1999 to 2001, he was involved in postdoctoral research at Chongqing University, where he is currently a professor. From November 1997 to April 1998, he was a research associate at the Chinese University of Hong Kong. From October 1999 to October 2000, he was a research associate at the City University of Hong Kong. From March 2001 to June 2001 and March 2002 to June 2002, he was a senior research associate at the City University of Hong Kong. From March 2006 to April 2007, he was a research fellow at the City University of Hong Kong. He has published more than 200 international journal and conference papers. His current research interests include neural networks, nonlinear dynamical systems, bifurcation and chaos, and cryptography.
Guo Chen received his B.E. and M.E. degrees in Computer Science and Engineering from Chongqing University, Chongqing, China, in 2003 and 2006, respectively, and his Ph.D. degree in Electrical Engineering from The University of Queensland, Brisbane, Australia, in 2010. He is now a Research Fellow at the School of Electrical and Information Engineering, the University of Sydney, Australia. Previously, he was a Research Fellow at The Australian National University. His research interests include optimization and control, complex network, dynamical systems, intelligent algorithms and their applications in smart grid.
Rights and permissions
About this article
Cite this article
Li, H., Liao, X. & Chen, G. Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics. Int. J. Control Autom. Syst. 11, 422–426 (2013). https://doi.org/10.1007/s12555-012-0100-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-012-0100-7