Abstract
Asynchronous switching differing from asynchronous consensus may hinder the system to reach a consensus. This receives very limited attention, especially when the multi-agent systems have a controller fault. In order to analyze the consensus in this situation, this paper studies the consensus of the second-order multi-agent systems under asynchronous switching with a controller fault. We convert the consensus problems under asynchronous switching into stability problems and obtain important results for consensus with the aid of linear matrix inequalities. An example is given to illustrate the effect of asynchronous switching on the consensus, and to validate the analytical results in this paper.
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Y. Yuan, H. Yuan, Z.Wang, L. Guo, and H. Yang, “Optimal control for networked control systems with disturbances: a delta operator approach,” IET Control Theory and Applications, vol. 11, no. 9, pp. 1325–1332, 2017.
J. Ota, “Multi–agent robot systems as distributed autonomous systems,” Advanced Engineering Informatics, vol. 20, no. 1, pp. 59–70, 2006.
M. Zhang, P. Tian, and X. Chen, “Unmanned aerial vehicle guidance law for ground target circumnavigation using range–based measurements,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 2455–2460, 2017.
R. Olfati–Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and timedelays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.
S.–X. Tang, J. Qi, and J. Zhang, “Formation tracking control for multi–agent systems: A wave–equation based approach,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2704–2713, 2017.
B. Zhu, C. Meng, and G. Hu, “Robust consensus tracking of double integrator dynamics by bounded distributed control,” International Journal of Robust and Nonlinear Control, vol. 26, no. 7, pp. 1489–1511, 2016.
D. Zheng, H. Zhang, J. Zhang, and G. Wang, “Consensus of multi–agent systems with faults and mismatches under switched topologies using a delta operator method,” Neurocomputing, vol. 315, pp. 198–209, 2018.
D. Ma and Y. Sun, “Finite–time circle surrounding control for multi–agent systems,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1536–1543, 2017.
B. Li, Z.–Q. Chen, C.–Y. Zhang, Z.–X. Liu, and Q. Zhang, “Containment control for directed networks multi–agent system with nonlinear dynamics and communication timedelays,” International Journal of Control, Automation and Systems, pp. 1–8, 2017.
D. Zheng and H. Zhang, “Research on the transformation of control protocols among three kinds of cooperative control for multi–agent systems,” Proc. of 8th International Conference on Intelligent Human–Machine Systems and Cybernetics (IHMSC), pp. 301–304, IEEE, 2016.
W. Liu and J. Huang, “Adaptive leader–following consensus for a class of higher–order nonlinear multi–agent systems with directed switching networks,” Automatica, vol. 79, pp. 84–92, 2017.
R. Olfati–Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi–agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007.
T. Li and J.–F. Zhang, “Mean square average–consensus under measurement noises and fixed topologies: Necessary and sufficient conditions,” Automatica, vol. 45, no. 8, pp. 1929–1936, 2009.
W. Ren and R.W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005.
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, 2010.
W. Hou, M. Fu, H. Zhang, and Z. Wu, “Consensus conditions for general second–order multi–agent systems with communication delay,” Automatica, vol. 75, pp. 293–298, 2017.
Y. Huang and Y. Jia, “Fixed–time consensus tracking control for second–order multi–agent systems with bounded input uncertainties via nfftsm,” IET Control Theory and Applications, vol. 11, no. 16, pp. 2900–2909, 2017.
C. Song, J. Cao, and Y. Liu, “Robust consensus of fractional–order multi–agent systems with positive real uncertainty via second–order neighbors information,” Neurocomputing, vol. 165, pp. 293–299, 2015.
X. Wu, Y. Tang, J. Cao, and W. Zhang, “Distributed consensus of stochastic delayed multi–agent systems under asynchronous switching,” IEEE Transactions on Cybernetics, vol. 46, no. 8, pp. 1817–1827, 2016.
F. Xiao and L. Wang, “Asynchronous consensus in continuous–time multi–agent systems with switching topology and time–varying delays,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1804–1816, 2008.
L. Fang and P. J. Antsaklis, “Asynchronous consensus protocols using nonlinear paracontractions theory,” IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2351–2355, 2008.
L. Lamport, “Lower bounds for asynchronous consensus,” Distributed Computing, vol. 19, no. 2, pp. 104–125, 2006.
Q. Zheng and H. Zhang, “Asynchronous H¥ fuzzy control for a class of switched nonlinear systems via switching fuzzy lyapunov function approach,” Neurocomputing, vol. 182, pp. 178–186, 2016.
L. Zhang and H. Gao, “Asynchronously switched control of switched linear systems with average dwell time,” Automatica, vol. 46, no. 5, pp. 953–958, 2010.
D. Zheng, H. Zhang, and Q. Zheng, “Consensus analysis of multi–agent systems under switching topologies by a topology–dependent average dwell time approach,” IET Control Theory and Applications, vol. 3, no. 3, pp. 429–438, 2017.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1990.
W. He and J. Cao, “Consensus control for high–order multi–agent systems,” IET Control Theory and Applications, vol. 5, no. 1, pp. 231–238, 2011.
Y. Cao and Y. Sun, “Consensus analysis for third–order multiagent systems in directed networks,” Mathematical Problems in Engineering, vol. 2015. 2015.
X. Zhao, L. Zhang, P. Shi, and M. Liu, “Stability and stabilization of switched linear systems with mode–dependent average dwell time,” IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1809–1815, 2012.
L. Xie, “Output feedback protect H¥ control of systems with parameter uncertainty,” International Journal of Control, vol. 63, no. 4, pp. 741–750, 1996.
H. Li, J. Wang, H. Du, and H. R. Karimi, “Adaptive sliding mode control for Takagi–Sugeno fuzzy systems and its applications,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 531–542, 2018.
Q. Zhou, H. Li, L. Wang, and R. Lu, “Prescribed performance observer–based adaptive fuzzy control for nonstrictfeedback stochastic nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 10, Oct. 2018.
Q. Zhou, L. Wang, C. Wu, and H. Li, “Adaptive fuzzy tracking control for a class of pure–feedback nonlinear systems with time–varying delay and unknown dead zone,” Fuzzy Sets and Systems, vol. 329, pp. 36–60, 2017.
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Recommended by Associate Editor Huaping Liu under the direction of Editor Hamid Reza Karimi. This work is supported by the National Natural Science Foundation of China( Grant No.61374117)
Dianhao Zheng received the B.Eng. degree in electronic science and technology from China University of Mining and Technology, Xuzhou, in 2009, and the M.S. degree in circuits and systems from University of Electronic Science and Technology of China, Chengdu, in 2012. He is currently working towards two Ph.D. degrees in circuits and systems at the University of Electronic Science and Technology of China and in engineering and information technology at the University of Technology Sydney. He was an engineer from 2012 to 2014. His research interests include cooperative control, multi-agent systems, and switched systems.
Hongbin Zhang received the B.Eng. degree in aerocraft design from Northwestern Polytechnical University, Xian, China, in 1999, and the MEng and PhD degrees in circuits and systems from the University of Electronic Science and Technology of China, Chengdu, in 2002 and 2006, respectively. He has been with the School of Electrical Engineering, University of Electronic Science and Technology of China, since 2002, where he is currently a professor. From August 2008 to August 2010, he has served as a research fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. His current research interests include intelligent control, autonomous cooperative control and integrated navigation.
J. Andrew Zhang received the B.Sc. degree from Xi’an JiaoTong University, China, in 1996, the M.Sc. degree from Nanjing University of Posts and Telecommunications, China, in 1999, and the Ph.D. degree from the Australian National University, in 2004. Currently, Dr. Zhang is an associate Professor in School of Computing and Communications, University of Technology Sydney, Australia. He was a researcher with Data 61, CSIRO, Australia from 2010 to 2016, the Networked Systems, NICTA, Australia from 2004 to 2010, and ZTE Corp, Nanjing, China from 1999 to 2001. Dr. Zhang’s research interests are in the area of signal processing for wireless communications and sensing, and autonomous vehicular networks. He has won 4 best paper awards for his work. He is a recipient of CSIRO Chairman’s Medal and the Australian Engineering Innovation Award in 2012 for exceptional research achievements in multi-gigabit wireless communications.
Yang Li received the B.E. degree in electronic and information engineering and M.S. degree in circuits and systemsfrom University of Electronic Science and Technology of China, Chengdu, in 2014 and 2017, respectively. He is currently working towards his Ph.D. degree in circuits and systems at the University of Electronic Science and Technology of China, Chengdu. His research interests include fuzzy control and switched systems.
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Zheng, D., Zhang, H., Andrew Zhang, J. et al. Consensus of the Second-order Multi-agent Systems under Asynchronous Switching with a Controller Fault. Int. J. Control Autom. Syst. 17, 136–144 (2019). https://doi.org/10.1007/s12555-018-0058-1
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DOI: https://doi.org/10.1007/s12555-018-0058-1