Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control

ZHAO Wei; REN Fengli

doi:10.21656/1000-0887.410190

Volume 42 Issue 3

Mar. 2021

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(3): 299-307

ZHAO Wei, REN Fengli. Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190

Citation:

ZHAO Wei, REN Fengli. Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190

Citation:

ZHAO Wei, REN Fengli. Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190

PDF( 784 KB)

Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control

doi: 10.21656/1000-0887.410190

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, P.R.China

Funds: The National Natural Science Foundation of China（61104031）

Received Date: 2020-06-20
Rev Recd Date: 2021-01-15
Publish Date: 2021-03-01

Abstract

Abstract

The finite-time and fixed-time consensus of multi-agent systems with bounded unknown acceleration was studied. Problems of double integrator dynamics under a leader with bounded unknowns were considered. Firstly, the protocol of pinning control was proposed. Then with the Lyapunov stability theory and the Filippov differential equations with discontinuous right hand sides, the sufficient conditions were provided to guarantee multi-agent consensus in finite time and fixed time. Finally, the numerical simulation of pinning consensus of multi-agent systems illustrates the effectiveness of the conditions.
- multi-agent system,
- pinning control,
- finite time,
- consensus,
- directed network

FullText(HTML)

References(29)

References

[1]	LI Z K, WEN G H, DUAN Z S, et al. Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs[J]. IEEE Transactions on Automatic Control,2015,60(4): 1152-1157.
[2]	LI Z K, REN W, LIU X D, et al. Distributed consensus of linear multi-agent systems with adaptive[J]. Automatica,2013,49(7): 1986-1995.
[3]	LI Z K, LIU X D. Distributed tracking control for linear multiagent systems with a leader of bounded unknown input[J]. IEEE Transactions on Automatic Control,2013,58(2): 518-523.
[4]	LI Z K, DING Z S. Distributed adaptive consensus and output tracking of unknown linear systems on directed graphs[J]. Automatica,2015,55: 12-18.
[5]	HONG Y G, HU J P, GAO L X. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica,2006,42(7): 1177-1182.
[6]	HONG Y G, CHEN G R, BUSHNELL L. Distributed observers design for leader-following control of multi-agent networks[J]. Automatica,2008,44(3): 846-850.
[7]	REN W, BEARD R W, ATKINS E M. Information consensus in multivehicle cooperative control: collective group behavior through local[J]. IEEE Control Systems Magazine,2007,27(2): 71-82.
[8]	周军, 童东兵, 陈巧玉. 基于事件触发控制带有多时变时滞的主从系统同步[J]. 应用数学和力学, 2019,40(12): 1389-1398. (ZHOU Jun, TONG Dongbing, CHEN Qiaoyu. Synchronization of master-slave systems with multiple time-varying delays based on the event-triggered mechanism[J]. Applied Mathematics and Mechanics,2019,40(12): 1389-1398. (in Chinese))
[9]	ZHOU J, LU J A, L J H. Pinning adaptive synchronization of a general complex dynamical network[J]. Automatica,2008,44(4): 996-1003.
[10]	CHEN T P, LIU X W, LU W L. Pinning complex networks by a single controller[J]. IEEE Transactions on Circuits and Systems Ⅰ: Regular Papers,2007,54(6): 1317-1326.
[11]	ZHOU J, WU X Q, YU W W, et al. Pinning synchronization of delayed neural networks[J]. Chaos: an Interdisciplinary Journal of Nonlinear Science,2008,18(4): 043111.
[12]	DU H B, WEN G H, WU D, et al. Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems[J]. Automatica,2020,113: 108797.
[13]	WEN G H, YU W W, CHEN Z Q, et al. Pinning a complex network to follow a target system with predesigned control inputs[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems Digital,2020,50(6): 2293-2304.
[14]	Lü H, HE W L, HAN Q L, et al. Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations[J]. Neural Networks,2019,116: 139-149.
[15]	CHEN F, CHEN Z Z, XIANG L Y, et al. Reaching a consensus via pinning control[J]. Automatica,2009,45(5): 1215-1220.
[16]	LIU X Y, HO D W C, SONG Q, et al. Finite/fixed-time pinning synchronization of complex networks with stochastic disturbances[J]. IEEE Transactions on Cybernetics,2019,49(6): 2398-2403.
[17]	LI S H, DU H B, LIN X. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics[J]. Automatica,2011,47(8): 1706-1712.
[18]	XIAO F, WANG L, CHEN J, et al. Finite-time formation control for multi-agent systems[J]. Automatica,2009,45(11): 2605-2611.
[19]	MENG Z Y, REN W, YOU Z. Distributed finite-time attitude containment control for multiple rigid bodies[J]. Automatica,2010,46(12): 2092-2099.
[20]	WANG L, XIAO F. Finite-time consensus problems for networks of dynamic agents[J]. IEEE Transactions on Automatic Control,2010,55(4): 950-955.
[21]	CORTS J. Finite-time convergent gradient flows with applications to network consensus[J]. Automatica,2006,42(11): 1993-2000.
[22]	CHEN G, LEWIS F L, XIE L H. Finite-time distributed consensus via binary control protocols[J]. Automatica,2011,〖STHZ〗 47(9): 1962-1968.
[23]	陈天平, 卢文联. 复杂网络协调性理论[M]. 北京: 高等教育出版社, 2013. (CHEN Tianping, LU Wenlian. Theory of Coordination in Complex Networks [M]. Beijing: Higher Education Press, 2013. (in Chinese))
[24]	洪奕光, 程代展. 非线性系统的分析与控制[M]. 北京: 科学出版社, 2005. (HONG Yiguang, CHENG Daizhan. Analysis and Control of Nonlinear Systems [M]. Beijing: Science Press, 2005. (in Chinese))
[25]	POLYAKOV A, EFIMOV D, PERRUQUETTI W. Finite-time and fixed-time stabilization: implicit Lyapunov function approach[J]. Automatica,2015,51: 332-340.
[26]	HARDY G, LITTLEWOOD J, PLYA G. Inequalities [M]. Cambridge: Cambridge University Press, 1952.
[27]	SHEN Y J, XIA X H. Semi-global finite-time observers for nonlinear systems[J]. Automatica,2008,44(12): 3152-3156.
[28]	ZHANG Y Y, YANG Y, ZHAO Y, et al. Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances[J]. International Journal of Control,2013,86(1): 29-40.
[29]	FILIPPOV A F. Differential Equations With Discontinuous Right-Hand Sides [M]. Dordrecht, Netherlands: Springer, 1988.