Abstract
This paper investigates the consensus problem of continuous-time leader-following nonlinear multi-agent systems with time-varying communication delay via reliable control. The parameter uncertainty is assumed to be bounded in given compact sets. With certain assumptions on the dynamic nonlinearity and underlying topology, the sufficient conditions are derived in terms of linear matrix inequality (LMI) by using a suitable Lyapunov- Krasovskii functional (LKF). It is ensure that the leader-following consensus can be achieved under the proposed reliable control scheme. Finally, numerical simulation results are presented to demonstrate the theoretical results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Z. Li and Z. Duan, Cooperative Control of Multi–agent Systems: A Consensus Region Approach, CRC Press, New York, 2014.
Z. Peng, G. Wen, S. Yang, and A. Rahmani, “Distributed consensus–based formation control for nonholonomic wheeled mobile robots using adaptive neural network,” Nonlinear Dynamimcs, vol. 86, no. 1, pp. 605–622, 2016.
S. Yang, Y. Cao, Z. Peng, G. Wen, and K. Guo, “Distributed formation control of nonholonomic autonomous vehicle via RBF neural network,” Mechanical Systems and Signal Processing, vol. 87, pp. 81–95, 2017.
H. Zhang, D. Yue, X. Yin, S. Hu, and C. X. Dou, “Finite–time distributed event–triggered consensus control for multi–agent systems,” Information Sciences, vol. 339, pp. 132–142, 2016.
D. Zhang, Z. Xu, Q. G. Wang, and Y. B. Zhao, “Leaderfollower H¥ consensus of linear multi–agent systems with aperiodic sampling and switching connected topologies,” ISA Transactions, vol. 68, pp. 150–159, 2017.
W. He, B. Zhang, Q. L. Han, F. Qian, J. Kurths, and J. Cao, “Leader–following consensus of nonlinear multiagent systems with stochastic sampling,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 327–338, 2017.
D. Li, J. Ma, H. Zhu, and M. Sun, “The consensus of multiagent systems with uncertainties and randomly occurring nonlinearities via impulsive control,” International Journal of Control, Automation and Systems, vol. 14, no. 4, pp. 1005–1011, 2016.
R. Rakkiyappan, B. Kaviarasan, and J. Cao, “Leaderfollowing consensus of multi–agent systems via sampleddata control with randomly missing data,” Neurocomputing, vol. 161, pp. 132–147, 2015.
M. Lu and L. Liu, “Consensus of linear multi–agent systems subject to communication delays and switching networks,” International Journal of Robust and Nonlinear Control, vol. 27, no. 9, pp. 1379–1396, 2017.
Y. Xu, S. Peng, and A. Guo, “Leader–following consensus of nonlinear delayed multi–agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input,” International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 566–576, 2018.
L. Li, D. W. Ho, and J. Lu, “Event–based network consensus with communication delays,” Nonlinear Dynamics, vol. 87, no. 3, pp. 1847–1858, 2017.
J. Qin, H. Gao, and W. X. Zheng, “Second–order consensus for multi–agent systems with switching topology and communication delay,” Systems & Control Letters, vol. 60, no. 6, pp. 390–397, 2011.
Q. Zhang, Y. Niu, L.Wang, L. Shen, and H. Zhu, “Average consensus seeking of high–order continuous–time multiagent systems with multiple time–varying communication delays,” International Journal of Control, Automation and Systems, vol. 9, no. 6, pp. 1209–1218, 2011.
H. S. Kim, J. B. Park, and Y. H. Joo, “Less conservative robust stabilization conditions for the uncertain polynomial fuzzy system under perfect and imperfect premise matching,” International Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1588–1598, 2016.
D. H. Lee, M. H. Tak, and Y. H. Joo, “A Lyapunov functional approach to robust stability analysis of continuoustime uncertain linear systems in polytopic domains,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 460–469, 2013.
R. Saravanakumar, M. S. Ali, H. Huang, J. Cao, and Y. H. Joo, “Robust H¥ state–feedback control for nonlinear uncertain systems with mixed time–varying delays,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 225–233, 2018.
C. Li, X. Liao, and R. Zhang, “Global robust asymptotical stability of multi–delayed interval neural networks: an LMI approach,” Physics Letters A, vol. 328, no. 6, pp. 452–462, 2004.
X. Xu, Z. Li, and L. Gao, “Distributed adaptive tracking control for multi–agent systems with uncertain dynamics,” Nonlinear Dynamics, vol. 90, no. 4, pp. 2729–2744, 2017.
Z. Li, Y. Zhao, and Z. Duan, “Distributed robust consensus of a class of Lipschitz nonlinear multi–agent systems with matching uncertainties,” Asian Journal of Control, vol. 1. no. 1, pp. 3–13, 2015.
Y. Wang, Y. Song, M. Krstic, and C. Wen, “Fault–tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single–way directed communication interactions and actuation failures,” Automatica, vol. 63, pp. 374–383, 2016.
C. H. Xie and G. H. Yang, “Cooperative guaranteed cost fault–tolerant control for multi–agent systems with timevarying actuator faults,” Neurocomputing, vol. 214, pp. 382–390, 2016.
G. Zhang, J. Qin, W. X. Zheng, and Y. Kang, “Faulttolerant coordination control for second–order multi–agent systems with partial actuator effectiveness,” Information Sciences, vol. 423, pp. 115–127, 2018.
O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “On stability analysis for neural networks with interval time–varying delays via some new augmented Lyapunov–Krasovskii functional,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3184–3201, 2014.
M. V. Thuan and V. N. Phat, “Optimal guaranteed cost control of linear systems with mixed interval time–varying delayed state and control,” Journal of Optimization Theory and Applications, vol. 152, no. 2, pp. 394–412, 2012.
H. Wu, X. Liao, W. Feng, S. Guo, and W. Zhang, “Robust stability analysis of uncertain systems with two additive time–varying delay components,” Applied Mathematical Modelling, vol. 33, no. 12, pp. 4345–4353, 2009.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Yang Tang under the direction of Editor Hamid Reza Karimi. This work was supported by Council of Scientific and Industrial Research, Govt. of India, New Delhi. Grant Number: 25(0273)/17/EMR-II dated 27.04.2017 and jointly supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education NRF-2016R1A6A1A03013567, NRF-2018R1A2A2A14023632) and by Korea Electric Power Corporation (Grant number: R18XA04).
K. Subramanian received the B.Sc and M.Sc degrees in mathematics from Sri Ramakrishna Mission Vidyalaya College of Arts and Science affiliated to Bharathiar University, Coimbatore, Tamilnadu, India, in 2011 and 2013, respectively. He received the Master of Philosophy from Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, India, in 2014. He is currently pursuing the Ph.D. degree with the Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamilnadu, India. His current research interests include neural networks, multi-agent systems and robust control theory.
P. Muthukumar received the Ph.D. degree from the Department of Mathematics, Gandhigram Rural Institute, Gandhigram, India, in 2009. Since 2010, he has been an Assistant Professor with the Department of Mathematics, Gandhigram Rural Institute. He was a Visiting Faculty, University of Texas at Arlington (UTA) Research Institute, TX, USA for a year. He was selected as a Visiting Faculty from the Research Center for Wind Energy Systems, Kunsan National University, Gunsan, Korea for three months in 2018. His current research interests include control theory, stochastic differential systems, and nonlinear control and its applications. Dr. Muthukumar was a recipient of the IUSSTF Research Fellow in 2012 from the DST, Govt. of India and the UGC-SAP Project Fellow Award in 2005 and the CSIRSRF Award in 2009 from the Indian Government.
Young Hoon Joo received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a professor in the Department of Control and Robotics Engineering, Kunsan National University, Korea. His major interest is mainly in the field of intelligent control, intelligent robot, human-robot interaction, wind-farm control, power system stabilization, and intelligent surveillance systems. He served as the President for Korea Institute of Intelligent Systems (KIIS) (2008-2009) and as the Editor-in-Chief for the International Journal of Control, Automation, and Systems (IJCAS) (2014-2017), and the Director of Research Center for Wind Energy Systems funded by Korean Government (2016-present) and the President of Korean Institute of Electrical Engineers (KIEE) (2019).
Rights and permissions
About this article
Cite this article
Subramanian, K., Muthukumar, P. & Joo, Y.H. Leader-following Consensus of Nonlinear Multi-agent Systems via Reliable Control with Time-varying Communication Delay. Int. J. Control Autom. Syst. 17, 298–306 (2019). https://doi.org/10.1007/s12555-018-0323-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-018-0323-3