The event-triggered consensus problem for observer-based second-order leader-following heterogeneous multi-agent systems with nonlinear term delay under input saturation conditions is investigated in this study. For a class of second-order leader-following heterogeneous multi-agent system models, the situation of agents with nonlinear delay terms in the system is considered. The observer is designed to reconstruct the state of the system. The structural state replaces the real state of the system to achieve the required state feedback, and the difference between the output quantities is inputted into the system as a feedback quantity (deviation) to achieve a better simulation. Considering the phenomenon of saturation control in many control systems, multi-agent consensus is achieved by combining saturation control and event-triggered pinning control in the controller. On the premise that each agent is affected by input saturation, an event-triggered pinning control protocol is designed to achieve the purpose of control by pinning down some key agents. The sufficient conditions for the second-order multi-agent system to achieve consensus are obtained by using the Lyapunov stability theory, algebraic Riccati equation, matrix theory, and other analytical techniques. The proposed event-triggered function can avoid Zeno behavior. The feasibility of the results is verified by numerical simulation.
Axel and Ruhe (1994) The rational krylov algorithm for nonsymmetric eigenvalue problems. iii: Complex shifts for real matrices. Bit Numerical Mathematics. 34: 165–176. DOI: 10.1007/BF01935024.
2.
BaldiSLiuDJainV, et al. (2020) Establishing platoons of bidirectional cooperative vehicles with engine limits and uncertain dynamics. IEEE Transactions on Intelligent Transportation Systems. 99(99): 1–13
3.
ChengLLiuWHouZG, et al. (2017) An adaptive takagi–sugeno fuzzy model-based predictive controller for piezoelectric actuators. IEEE Transactions on Industrial Electronics64(4): 3048–3058. DOI: 10.1109/tie.2016.2644603.
4.
DingLZhengWXGuoG (2018) Network-based practical set consensus of multi-agent systems subject to input saturation. Automatica89: 316–324. DOI: 10.1016/j.automatica.2017.12.001.
5.
DongXHuG (2016) Time-varying formation control for general linear multi-agent systems with switching directed topologies. Automatica73: 47–55. DOI: 10.1016/j.automatica.2016.06.024.
6.
DuHWenGWuD, et al. (2020) Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems. Automatica113: 108797. DOI: 10.1016/j.automatica.2019.108797.
7.
FengTTWuGXuTT (2015) An inexact shift-and-invert arnoldi algorithm for large non-hermitian generalised toeplitz eigenproblems. East Asian Journal on Applied Mathematics5(02): 160–175. DOI: 10.4208/eajam.010914.130415a.
8.
FuJWenGYuW, et al. (2018) Finite-time consensus for second-order multi-agent systems with input saturation. IEEE Transactions on Circuits and Systems II: Express Briefs65(11): 1758–1762. DOI: 10.1109/TCSII.2017.2759193.
9.
GuanZHSunFLWangYW, et al. (2012) Finite-time consensus for leader-following second-order multi-agent networks. IEEE Transactions on Circuits & Systems I Regular Papers59(11): 2646–2654. DOI: 10.1109/TCSI.2012.2190676.
10.
HanTGuanZHXiaoB, et al. (2019) Distributed output consensus of heterogeneous multi-agent systems via an output regulation approach. Neurocomputing360: 131–137. DOI: 10.1016/j.neucom.2019.06.028.
11.
HaoLZhanXWuJ, et al. (2020) Bipartite finite time and fixed time output consensus of heterogeneous multiagent systems under state feedback control. Circuits and Systems II: Express Briefs, IEEE Transactions on circuits99(99): 1–1. DOI: 10.1109/TCSII.2020.3047483.
12.
HeinMBühlerT (2010) An inverse power method for nonlinear eigenproblems with applications in 1-spectral clustering and sparse pca. Frontiers in Artificial Intelligence & Applications272: 847–855. DOI: 10.3233/978-1-61499-472-5-343.
13.
HongYHuJGaoL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica42(7): 1177–1182. DOI: 10.1016/j.automatica.2006.02.013.
14.
HuifenH, WenwuYuJunjieFu. et al. (2018) A novel class of distributed fixed-time consensus protocols for second-order nonlinear and disturbed multi-agent systems. IEEE Transactions on Network Science and Engineering6(4): 760–772. DOI: 10.1109/TNSE.2018.2873060.
15.
JiangWRahmaniAWenG (2019) Fully distributed time-varying formation-containment control for large-scale nonholonomic vehicles with an unknown real leader. International Journal of Control94: 1–22. DOI: 10.1080/00207179.2019.1626996.
16.
JLiuCWLiXCaiX (2019) Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics. Journal of the Franklin Institute356(6): 3217–3244. DOI: 10.1016/j.jfranklin.2019.01.020.
17.
KaviarasanBSakthivelRWangC, et al. (2018) Resilient control design for consensus of nonlinear multi-agent systems with switching topology and randomly varying communication delays. Neurocomputing311: 155–163. DOI: 10.1016/j.neucom.2018.05.054.
18.
LiSJieZLiX, et al. (2017) Formation control of heterogeneous discrete-time nonlinear multi-agent systems with uncertainties. IEEE Transactions on Industrial Electronics64(6): 4730–4740. DOI: 10.1109/TIE.2017.2674590.
19.
LiYXiangJWeiW (2011) Consensus problems for linear time-invariant multi-agent systems with saturation constraints. Iet Control Theory & Applications5(6): 823–829. DOI: 10.1049/iet-cta.2009.0299.
20.
LinZ (1998) Low gain feedback. Lecture Notes in Control & Information Sciences. DOI: 10.1007/3-540-68383-6.
21.
LiuKXieGRenW, et al. (2013) Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies. Systems and Control Letters62(2): 152–162. DOI: 10.1016/j.sysconle.2012.11.003.
22.
LiuXHoDCaoJ, et al. (2017) Discontinuous observers design for finite-time consensus of multiagent systems with external disturbances. IEEE Transactions on Neural Networks and Learning Systems28(11): 2826–2830. DOI: 10.1109/TNNLS.2016.2599199.
23.
MiaoGMaQ (2015) Group consensus of the first-order multi-agent systems with nonlinear input constraints. Neurocomputing161: 113–119. DOI: 10.1016/j.neucom.2015.02.058.
24.
PostoyanRAntaAHeemelsW, et al. (2013) Periodic event-triggered control for nonlinear systems. Periodic event-Triggered Control for Nonlinear SystemsPiscataway, NJ: IEEE. 7397–7402. DOI: 10.1109/CDC.2013.6761063.
25.
QinJFuWZhengWX, et al. (2017a) On the bipartite consensus for generic linear multiagent systems with input saturation. IEEE Transactions on Cybernetics47(8): 1948–1958. DOI: 10.1109/TCYB.2016.2612482.
26.
QinLHeXZhouD (2017b) Distributed proportion-integration-derivation formation control for second-order multi-agent systems with communication time delays. Neurocomputing267(6): 271–282. DOI: 10.1016/j.neucom.2017.05.088.
27.
RenJSongQGaoY, et al. (2019) Leader-following bipartite consensus of second-order time-delay nonlinear multi-agent systems with event-triggered pinning control under signed digraph. Neurocomputing385: 186–196. DOI: 10.1016/j.neucom.2019.12.043.
28.
SongQCaoJYuW (2010) Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Systems & Control Letters59(9): 553–562. DOI: 10.1016/j.sysconle.2010.06.016.
29.
SuHChenGWangX, et al. (2011) Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica47(2): 368–375. DOI: 10.1016/j.automatica.2010.10.050.
30.
SuHChenMZQLamJ, et al. (2013) Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Transactions on Circuits & Systems I Regular Papers60(7): 1881–1889. DOI: 10.1109/TCSI.2012.2226490.
31.
ValcherMEMisraP (2014) On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Systems & Control Letters66: 94–103. DOI: 10.1016/j.sysconle.2014.01.006.
32.
VicsekTCzirokABen-JacobE, et al. (1995) Novel type of phase transition in a system of self-driven particles. Physical Review Letters75(6). 11. DOI: 10.1103/PhysRevLett.75.1226.
33.
WangXSuHWangX, et al. (2017) Fully distributed event-triggered semiglobal consensus of multi-agent systems with input saturation. IEEE Transactions on Industrial Electronics64(6): 5055–5064. DOI: 10.1109/TIE.2016.2642879.
34.
WangYL (2010) Group consensus in multi-agent systems with switching topologies and communication delays. Systems & Control Letters59(6): 340–348. DOI: 10.1016/j.sysconle.2010.03.009.
35.
WuZXuYPanY, et al. (2017) Event-triggered pinning control for consensus of multiagent systems with quantized information. IEEE Transactions on Systems, Man, and Cybernetics: Systems48(11): 1929–1938. DOI: 10.1109/TSMC.2017.2773634.
36.
XiaoZFanX (2021) Bearing-based Formation Control of Multi-Agents with Dual-Leaders StructurePiscataway, NJ: IEEE. DOI: 10.1109/CCDC52312.2021.9602036.
37.
XieYNaHMaC (2014) Iterative method to solve the generalized coupled sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix. Computers & Mathematics with Applications67(11): 2071–2084. DOI: 10.1016/j.camwa.2014.04.012.
38.
YangTMengZDimarogonasDV, et al. (2014) Global consensus for discrete-time multi-agent systems with input saturation constraints. Automatica50(2): 499–506. DOI: 10.1016/j.automatica.2013.11.008.
39.
ZamanianMAbdollahiFNikraveshSKY (2021) Adaptive consensus for heterogeneous unknown nonlinear multi-agent systems with asymmetric input dead-zone: A finite-time approach. Transactions of the Institute of Measurement and Control44(1): 105–120. DOI: 10.1177/01423312211024006.
40.
ZegersJCSemsar-KazerooniEPloegJ, et al. (2017) Consensus control for vehicular platooning with velocity constraints. IEEE Transactions on Control Systems Technology99(99): 1–14. PP(
41.
ZhangBLHanQLZhangXM (2017) Recent advances in vibration control of offshore platforms. Nonlinear Dynamics89: 755–771. DOI: 10.1007/s11071-017-3503-4.
42.
ZhangHFengGYanH, et al. (2014) Observer-based output feedback event-triggered control for consensus of multi-agent systems. IEEE Transactions on Industrial Electronics61(9): 4885–4894. DOI: 10.1109/TIE.2013.2290757.
43.
ZhengYMaJWangL (2017) Consensus of hybrid multi-agent systems. IEEE Transactions on Neural Networks & Learning Systems29(4): 1359–1365. DOI: 10.1109/TNNLS.2017.2651402.
44.
ZhengYZhaoQMaJ, et al. (2019) Second-order consensus of hybrid multi-agent systems. Systems & Control Letters125: 51–58. DOI: 10.1016/j.sysconle.2019.01.009.
45.
ZhengYSZhuYWangL (2011) Consensus of heterogeneous multi-agent systems. IET Control Theory and Applications5(16): 1881–1888. DOI: 10.1049/iet-cta.2011.0033.
46.
ZhouBLinZ (2014) Consensus of high-order multi-agent systems with large input and communication delays. Automatica50(2): 452–464. DOI: 10.1016/j.automatica.2013.12.006.
