Abstract
In this paper, the consensus problem of leader-following nonlinear multi-agent systems with packet dropout is addressed. The iterative learning control method is applied to design the control protocol. Then, a distributed control protocol is presented, and a sufficient condition is derived. In addition, the Bernoulli distribution process is introduced to model the packet dropout case, where the dropout rate is converted into a stochastic parameter. The convergence of proposed control protocol is analyzed by norm theory. It is proved that, when there exists the packet dropout, the output of all the following agents can track the trajectory of leader under the proposed control protocol. Finally, two examples are provided to illustrate the validity of the theoretical analysis.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Postoyan, M. Bragagnolo, E. Galbrun, J. Daafouz, D. Nešić, and E. Castelan, “Event-triggered tracking control of unicycle mobile robots,” Automatica, vol. 52, pp. 302–308, 2015.
X. W. Dong, Y. Zhou, Z. Ren, and Y. S. Zhong, “Time-varying formation control for unmanned aerial vehicles with switching interaction topologies,” Control Engineering Practice, vol. 46, 26–36, 2016.
H. B. Gao, B. Chen, J. Q. Wang, K. Q. Li, J. H. Zhao, and D. Y. Li, “Object classification using CNN-based fusion of vision and LIDAR in autonomous vehicle environment,” IEEE Transactions on Industrial Informatics, vol. 14, no. 9, pp. 4224–4231, 2018.
G. T. Xie, H. B. Gao, L. J. Qian, B. Huang, K. Q. Li, and J. Q. Wang, “Vehicle trajectory prediction by integrating physics-and maneuver-based approaches using interactive multiple model,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7, pp. 5999–6008, 2018.
D. Y. Li and H. B. Gao, “A Hardware Platform Framework for an Intelligent Vehicle Based on a Driving Brain,” Engineering, vol. 4, no. 4, pp. 464–470, 2018.
Z. Z. Zhong, L. N. Sun, J. C. Wang, P. H. Lv, and H. J. Zheng, “Consensus for first- and second-order discretetime multi-agent systems with delays based on model predictive control schemes,” Circuits, Systems and Signal Processing, vol. 34, no. 1, pp. 127–152, 2015.
H. J. Li and H. Y. Su, “Second-order consensus in multi-agent systems with directed topologies and communication constraints,” Neurocomputing, vol. 173, pp. 942–952, 2016.
H. Haghshenas, M. A. Badamchizadeh, and M. Baradarannia, “Containment control of heterogeneous linear multi-agent systems,” Automatica, vol. 54, pp. 210–216, 2015.
Y. Cui and Y. Jia, “L2L∞ consensus control for high-order multi-agent systems with switching topologies and time-varying delays,” IET Control Theory & Applications, vol. 6, no. 12, pp. 1933–1940, 2012.
J. Q. Hu, J. D. Cao, K. Yuan, and T. Hayat, “Cooperative tracking for nonlinear multi-agent systems with hybrid time-delayed protocol,” Neurocomputing, vol. 171, pp. 171–78, 2016.
J. J. Fu and J. Z. Wang, “Adaptive consensus tracking of high-order nonlinear multi-agent systems with directed communication graphs,” International Journal of Control, Automation, and Systems, vol. 12, no. 5, pp. 919–929, 2014.
B. H. Wang, J. C. Wang, L. W. Zhang, and B. Zhang, “Robust adaptive consensus tracking for higher-order multi-agent uncertain systems with nonlinear dynamics via distributed intermittent communication protocol,” International Journal of Adaptive Control and Signal Processing, vol. 30, no. 3, pp. 511–533, 2016.
W. X. Li, Z. Q. Chen, Z. X. Liu, “Output regulation distributed formation control for nonlinear multi-agent systems,” Nonlinear Dynamics, vol. 78, no. 2, pp. 1339–1348, 2014.
R. S. Dong and Z. Y. Geng, “Consensus for formation control of multi-agent systems,” International Journal of Robust and Nonlinear Control, vol. 25, no. 14, pp. 2481–2501, 2015.
S. Hu and W. Y. Yan, “Stability robustness of networked control systems with respect to packet loss,” Automatica, vol. 43, no. 7, pp. 1243–1248, 2007.
L. Zhou and G. P. Lu, “Stabilization for nonlinear systems via a limited capacity communication channel with data packet dropout,” Journal of Control Theory and Applications, vol. 8, no. 1, pp. 111–116, 2010.
Y. Song, J. C. Wang, Y. H. Shi, and C. Li, “Packet-loss-dependent stabilization of NCSs with network-induced delay and packet dropout,” Journal of Systems Engineering and Electronics, vol. 23, no. 3, pp. 408–413, 2012.
X. Gong, Y. J. Pan, and A. Pawar, “A novel leader following consensus approach for multi-agent systems with packet loss,” International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp. 763–775, 2017.
X. Gong, Y. J. Pan, J. N. Li, and H. Y. Su, “Leader following consensus for multi-agent systems with stochastic packet dropout,” Proceedings of the 10th IEEE International Conference on Control and Automation, pp. 1160–1165, 2013.
Z. X. Liu, X. You, H. J. Yang, and L. Zhao, “Leader-following consensus of heterogeneous multi-agent systems with packet dropout,” International Journal of Control, Automation, and Systems, vol. 13, no. 5, pp. 1067–1075, 2015.
W. B. Zhang, Y. Tang, T. W. Huang, and J. Kurths, “Sampled-data consensus of linear multi-agent systems with packet losses,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2516–2527, 2017.
D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96–14, 2006.
S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” Journal of Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984.
C. Zhang and J. Li, “Adaptive iterative learning control of non-uniform trajectory tracking for strict feedback nonlinear time-varying systems with unknown control direction,” Applied Mathematical Modelling, vol. 39, no. 10–11, pp. 2942–2950, 2015.
X. H. Bu, Z. S. Hou, and F. S. Yu, “Stability of first and high order iterative learning control with data dropouts,” International Journal of Control, Automation, and Systems, vol. 9, no. 5, pp. 843–849, 2011.
B. L. Wu, D. W. Wang, E. K. Poh, “High precision satellite attitude tracking control via iterative learning control,” Journal of Guidance Control and Dynamics, vol. 38, no. 3, pp. 528–533, 2015.
X. F. Deng, X. X. Sun, R. Liu, and S. G. Liu, “Consensus control of leader-following nonlinear multi-agent systems with distributed adaptive iterative learning control,” International Journal of Systems Science, vol. 49, no. 16, pp. 3247–3260, 2018.
X. F. Deng, X. X. Sun, and R. Liu, “Quantized consensus control for second-order nonlinear multi-agent systems with sliding mode iterative learning approach,” International Journal of Aeronautical and Space Sciences, vol. 19, no. 2, pp. 19:518–533, 2018.
Y. Liu and Y. M. Jia, “An iterative learning approach to formation control of multi-agent systems,” Systems & Control Letters, vol. 61, no. 1, pp. 148–154, 2012.
X. F. Deng, X. X. Sun, R. Liu, and S. G. Liu, “Consensus control of time-varying delayed multiagent systems with high-order iterative learning control,” International Journal of Aerospace Engineering, vol. 2018, Article ID 4865745, 12 pages, 2018.
J. Xu, “Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking,” Systems & Control Letters, vol. 89, pp. 16–23, 2016.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Augie Widyotriatmo under the direction of Editor Myo Taeg Lim. This work is supported by the Aeronautical Science Foundation of China (20155896025).
Xiongfeng Deng received the B.S. and M.S. degrees from Anhui Polytechnic University and Shaanxi University of Science & Technology, China, in 2012 and 2015, respectively. He is currently pursuing a Ph.D. degree in Control Science and Engineering from Air Force Engineering University, China. His main research interests include cooperative control of multi-agent systems and iterative learning control.
Xiuxia Sun received the Ph.D. degree in Control Science and Engineering from Beihang University, China, in 1999. She is working as a Professor in the Equipment Management and Unmanned Aerial Vehicle Engineering College, Air Force Engineering University, China. Her research fields are robust control, adaptive control and flight control.
Shuguang Liu is working as an Associate Professor in the Equipment Management and Unmanned Aerial Vehicle Engineering College, Air Force Engineering University. His research interests include flight control and formation control of unmanned aerial vehicle.
Rights and permissions
About this article
Cite this article
Deng, X., Sun, X. & Liu, S. Iterative Learning Control for Leader-following Consensus of Nonlinear Multi-agent Systems with Packet Dropout. Int. J. Control Autom. Syst. 17, 2135–2144 (2019). https://doi.org/10.1007/s12555-018-0329-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-018-0329-x