Event-Triggered Leader-Following Tracking Control of Multi-Agent Systems with Multivariable Single Integrator Dynamics


School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran


In this paper, the communications between follower agents in the leader-following tracking control of Multi-agent systems with multivariable single integrator dynamics, are reduced. A fully distributed control scheme is proposed in which a local non-combinational decision variable (DV) is continuously observed. If the norm of the DV’s measurement error violates a time-dependent threshold, an event is occurred and the DV is sampled, stored in a data store unit (DSU) and sent to a neighbor-to-neighbor low bandwidth communication network (CN). Also, the last sampled neighbors’ data received from the CN, are stored in the DSU. A control law computed from the last stored data, is fed to the agents’ dynamics. It is shown that under this control law and by using the proposed event-triggering mechanism, the follower agents’ tracking error remains bounded and the resultant closed-loop system does not exhibit Zeno behavior. The numerical simulation is included to verify the effectiveness of the proposed control scheme.


[1] R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. Automat. Contr., vol. 49, no. 9, pp. 1520–1533, 2004.
[2] W. Ren and R. W. Beard, Distributed consensus in multi-vehicle cooperative control. Springer, 2008.
[3] Q. Yang, J. A. Barria and T. C. Green, “Communication infrastructures for distributed control of power distribution networks,” IEEE Trans. Ind. Informatics, vol. 7, no. 2, pp. 316–327, 2011.
[4] W. Heemels, K. H. Johansson and P. Tabuada, “An introduction to event-triggered and self-triggered control,” in Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, pp. 3270–3285, 2012.
[5] P. Tabuada, “Event-triggered real-time scheduling of stabilizing control tasks,” IEEE Trans. Automat. Contr., vol. 52, no. 9, pp. 1680–1685, 2007.
[6] D. V Dimarogonas, E. Frazzoli and K. H. Johansson, “Distributed event-triggered control for multi-agent systems,” IEEE Trans. Automat. Contr., vol. 57, no. 5, pp. 1291–1297, 2012.
[7] G. S. Seyboth, D. V Dimarogonas and K. H. Johansson, “Event-based broadcasting for multi-agent average consensus,” Automatica, vol. 49, no. 1, pp. 245–252, 2013.
[8] Y. Fan, G. Feng, Y. Wang and C. Song, “Distributed event-triggered control of multi-agent systems with combinational measurements,” Automatica, vol. 49, no. 2, pp. 671–675, 2013.
[9] E. Garcia, Y. Cao and D. W. Casbeer, “Decentralized event-triggered consensus with general linear dynamics,” Automatica, vol. 50, no. 10, pp. 2633–2640, 2014.
[10] فرهاد بیات و صالح مبیّن، «ردیابی مقید مبتنی بر کنترل‌کننده پیش‌بین با هزینه محاسباتی کم: رویکرد برنامه‌ریزی پارامتری»، مجله مهندسی برق دانشگاه تبریز، جلد 46، شماره 4، صفحات 47-39، زمستان 1395.
[11] Y. Hong, J. Hu and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006.
[12] J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with coupling time delays,” Phys. A Stat. Mech. its Appl., vol. 374, no. 2, pp. 853–863, 2007.
[13] A. Bidram, F. L. Lewis and A. Davoudi, “Synchronization of nonlinear heterogeneous cooperative systems using input–output feedback linearization,” Automatica, vol. 50, no. 10, pp. 2578–2585, 2014.
[14] W. Zhu and Z.-P. Jiang, “Event-based leader-following consensus of multi-agent systems with input time delay,” IEEE Trans. Automat. Contr., vol. 60, no. 5, pp. 1362–1367, 2015.
[15] A. Adaldo et al., “Event-triggered pinning control of switching networks,” IEEE Trans. Control Netw. Syst., vol. 2, no. 2, pp. 204–213, 2015.
[16] Y. Cheng and V. Ugrinovskii, “Event-triggered leader-following tracking control for multivariable multi-agent systems,” Automatica, vol. 70, pp. 204–210, 2016.
[17] S. Mobayen and V. J. Majd, “Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances,” Nonlinear Dyn., vol. 70, no. 1, pp. 171–180, 2012.
[18] بدرالزمان حسینی، مهدی سجودی و عباس چترایی، «طراحی مشاهده‌گر مقاوم و کنترل‌گر فیدبک خروجی برای سیستم‌های چندعاملی دارای تأخیر بازه‌ای و متأثر از نامعینی و اغتشاش»، مجله مهندسی برق دانشگاه تبریز، جلد 46، شماره 1، صفحات 120-99، بهار 1395.
[19] W.H. Steeb and T. K. Shi, Matrix calculus and Kronecker product with applications and C++ programs. World Scientific, 1997.
[20] H. K. Khalil, Noninear Systems. Prentice-Hall, New Jersey, 1996.