Abstract
An event-triggered distributed model predictive control (DMPC) approach for a type of dynamically decoupled, independently constrained systems with a coupled performance objective, is presented. The approach employs, for each agent, a compatibility constraint (in the spirit of Dunbar and Murray) in the optimization problem. An event-triggering condition, based-on the overall stability condition of the system, is developed. If the triggering condition for an agent is satisfied, then the agent solves its optimization problem; otherwise, then the agent retain feasibility and stability by simply adopting the tail of its previous solutions. A simulation example is provided to illustrate the effectiveness of the provided approach.
Similar content being viewed by others
References
H. T. Zhang, Z. M. Cheng, G. R. Chen, and C. G. Li, “Model predictive flocking control for second-order multi-agent systems with input constraints,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 6, pp. 1599–1606, June 2015.
X. D. Zhang, S. S. Gao, X. P. Liu, and T. P. Huang, “Distributed dual-rate consensus predictive control of looper tension system in hot rolling mills,” International Journal of Control Automation and Systems, vol. 16, no. 5, pp. 577–585, March 2018.
H. Q. Pei, S. M. Chen, and Q. Lai, “A local flocking algorithm of multi-agent dynamic systems,” International Journal of Control, vol. 88, no. 11, pp. 1–23, April 2015.
H. J. Liang, H. W. Zhang, and Z. S. Wang, “Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems,” ISA Transactions, vol. 59, pp. 72–78, September 2015.
T. Li, F. Wu, and J. F. Zhang, “Multi-Agent consensus with relative-state-dependent measurement noises,” IEEE Transactions on Automatic Control, vol. 59, no. 9, pp. 2463–2468, September 2014.
J. L. Wang and H. N. Wu, “Leader-following formation control of multi-agent systems under fixed and switching topologies,” International Journal of Control, vol. 85, no. 6, pp. 695–705, June 2012.
B. Zhu, A. H. B. Zaini, and L. Xie, “Distributed guidance for interception by using multiple rotary-wing unmanned aerial vehicles,” International Journal of Control, vol. 64, no. 7, pp. 5648–5656, July 2017.
X. B. Ping, P. Wang, and J. F. Zhang, “A multi-step output feedback robust MPC approach for LPV systems with bounded parameter changes and disturbance,” International Journal of Control Automation and Systems, vol. 16, no. 5, pp. 2157–2168, September 2018.
P. Bumroongsri, “Tube-based robust MPC for linear time-varying systems with bounded disturbances,” International Journal of Control Automation and Systems, vol. 13, no. 3, pp. 620–625, June 2015.
P. Y. Zhang, D. W. Li, Y. G. Xi, and J. Zhang, “Improved model prediction and RMPC design for LPV systems with bounded parameter changes,” Automatica, vol. 49, no. 12, pp. 3695–3699, December 2013.
S. Y. Yu, C. Maier, H. Chen, and F. Allgöwer, “Tube MPC scheme based on robust control invariant set with application to Lipschitz nonlinear systems,” Systems & Control Letters, vol. 62, no. 2, pp. 194–200, February 2013.
X. Liu, D. Constantinescu, and Y. Shi, “Robust model predictive control of constrained non-linear systems: adopting the non-squared integrand objective function,” IET Control Theory and Applications, vol. 9, no. 5, pp. 649–658, March 2015.
D. F. He, H. Huang, and Q. X. Chen, “Quasi-min-max MPC for constrained nonlinear systems with guaranteed input-to-state stability,” Journal of the Franklin Institute, vol. 351, no. 6, pp. 3405–3423, June 2014.
B. C. Ding, L. H. Xie, and W. J. Cai, “Distributed model predictive control for constrained linear systems,” International Journal of Robust and Nonlinear Control, vol. 20, no. 11, pp. 1285–1298, November 2010.
Y. Zheng, J. Z. Zhou, Y. H. Xu, Y. C. Zhang, and Z. D. Qian, “A distributed model predictive control based load frequency control scheme for multi-area interconnected power system using discrete-time laguerre functions,” ISA Transcations, vol. 68, no. 5, pp. 127–140, March 2017.
H. P. Li and W. S. Yan, “Receding horizon control based consensus scheme in general linear multi-agent systems,” Automatica, vol. 56, pp. 12–18, March 2015.
C. X. Liu, J. Gao, and D. M. Xu, “Lyapunov-based model predictive control for tracking of nonholonomic mobile robots under input constraints,” International Journal of Control Automation and Systems, vol. 15, no. 5, pp. 2313–2319, July 2017.
W. B. Dunbar and R. M. Murray, “Distributed receding horizon control for multi-vehicle formation stabilization,” Automatica, vol. 42, no. 4, pp. 549–558, April 2006.
G. Chaloulos, P. Hokayem, and J. Lygeros, “Distributed hierarchical MPC for conflict resolution in air traffic control,” Proceedings of the 2010 American Control Conference, pp. 3945–3950, July 2010.
L. F. Zhou and S. Y. Li, “Distributed model predictive control for consensus of sampled-data multi-agent systems with double-integrator dynamics,” IET Control Theory and Applications, vol. 9, no. 12, pp. 1774–1780, August 2015.
M. Zhao and B. C. Ding, “Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics,” ISA Transactions, vol. 5, no. 11, pp. 1–12, March 2015.
D. V. Dimarogonas, E. Frazzoli, and K. H. Johansson, “Distributed eventtriggered control for multi-agent systems,” IEEE Transactions on Automatic Control, vol. 57, no. 5, pp. 1291–1297, May 2012.
W. Zhu and Z. P. Jiang, “Event-based leader-following consensus of multi-agent systems with input time delay,” IEEE Transactions on Automatic Control, vol. 60, no. 5, pp. 1362–1367, May 2015.
Y. Y. Zou, X. Su, and Y. G. Niu, “Event-triggered distributed predictive control for the cooperation of multiagent systems,” IET Control Theory and Applications, vol. 11, no. 1, pp. 10–16, January 2017.
X. X. Mi, Y. Y. Zou, S. Y. Li, and H. R. Karimi, “Self-triggered DMPC design for cooperative multi-agent systems,” IEEE Transactions on Industrial Electronics, vol. 67, no. 1, pp. 512–520, January. 2020.
H. P. Li, W. S. Yan, Y. Shi, and Y. T. Wang, “Periodic event-triggering in distributed receding horizon control of nonlinear systems” Systems & Control Letters, vol. 86, pp. 16–23, December 2015.
M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. 10, pp. 1361–1379, 1996.
H. H. J. Bloemen, T. J. J. van de Boom, and H. B. Verbruggen, “Optimizing the end-point state-weighting matrix in model predictive control,” Automatica, vol. 38, no. 6, pp. 1061–1068, 2002.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Recommended by Associate Editor Guangdeng Zong under the direction of Editor Jay H. Lee. This work was supported by the National Natural Science Foundation of China (62073053), the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization under Grant U1809207, and the Research Project of Chongqing Science and Technology Commission (cstc2018jcyjAX0691).
Xiaoming Tang received his B.S. degree in automation from the College of Information and Electrical Engineering, Panzhihua University, China, in 2008, and a Ph.D. degree in control theory and control engineering from the College of Automation, Chongqing University, Chongqing, China, in 2013. From March 2016 to March 2017, he carried out his Postdoctoral research in University of Texas at Arlington, Texas, USA. He is currently an Associate Professor with the College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, China. His current research interests include model predictive control and networked control systems.
Mengyue Li received her B.S. degree in electrical engineering and automation from Henan Normal University, Henan, China, in 2018. She is currently pursuing an M.S. degree in control science and engineering with the College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, China. Her current research interests include model predictive control and networked control systems.
Shanbi Wei received his B.S. degree from the Chongqing University, Chongqing, China, in 2003, and a Ph.D. degree from the Chongqing University, Chongqing, China, in 2009. He is currently an Associate Professor with the College of Automation, Chongqing University, China. His research interests include distributed model predictive control and networked control systems.
Baocang Ding received his B.S. degree from the China University of Petroleum, Beijing, in 2000, and a Ph.D. degree from Shanghai Jiao Tong University, in 2003. From September 2005 to September 2006, he was a Postdoctoral Research Fellow with the Department of Chemical and Materials Engineering, University of Alberta, Canada. From November 2006 to August 2007, he was a Research Fellow with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. From September 2003 to August 2007, he was an Associate Professor with the Hebei University of Technology, Tianjin, China. From September 2007 to December 2008, he was a Professor with Chongqing University, Chongqing, China. From January 2009 to October 2019, he was a Professor with Xi’an Jiaotong University, Xi’an, China. He is currently a Professor with the Chongqing University of Posts and Telecommunications. His research interests include predictive control, fuzzy control, networked control, and distributed control systems.
Rights and permissions
About this article
Cite this article
Tang, X., Li, M., Wei, S. et al. Event-triggered Synchronous Distributed Model Predictive Control for Multi-agent Systems. Int. J. Control Autom. Syst. 19, 1273–1282 (2021). https://doi.org/10.1007/s12555-019-0795-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-019-0795-9