离散时间分数阶多自主体系统的时延一致性

杨洪勇; 郭雷; 张玉玲; 姚秀明

doi:10.3724/SP.J.1004.2014.02022

离散时间分数阶多自主体系统的时延一致性

doi: 10.3724/SP.J.1004.2014.02022

杨洪勇^1,2, ,,
郭雷²,
张玉玲¹,
姚秀明²

1.
鲁东大学信息与电气工程学院烟台 264025;
2.
北京航空航天大学自动化科学与电气工程学院北京 100191

基金项目:

国家重点基础研究发展计划（973计划）（2012CB720003），国家自然科学基金（91016004，61273152，61203041，61127007），山东省自然科学基金（ZR2011FM017，ZR2013FL007）资助

详细信息

作者简介:
杨洪勇鲁东大学信息与电气工程学院教授.2005年于东南大学自动化系获得工学博士学位，现在北京航空航天大学自动化科学与电气工程学院飞行器控制一体化技术国家级重点实验室做博士后研究工作.主要研究方向为复杂网络，多智能体编队，智能控制.本文通信作者.E-mail：hyyang@yeah.net

通讯作者:
杨洪勇鲁东大学信息与电气工程学院教授.2005年于东南大学自动化系获得工学博士学位，现在北京航空航天大学自动化科学与电气工程学院飞行器控制一体化技术国家级重点实验室做博士后研究工作.主要研究方向为复杂网络，多智能体编队，智能控制.本文通信作者.E-mail：hyyang@yeah.net

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- 被引次数: 0
出版历程
- 收稿日期: 2013-06-17
- 修回日期: 2014-03-14
- 刊出日期: 2014-09-20

Delay Consensus of Fractional-order Multi-agent Systems with Sampling Delays

1.
School of Information and Electrical Engineering, Ludong University, Yantai 264025;
2.
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191

Funds:

Supported by National Basic Research Program of China (973 Program) (2012CB720003), National Natural Science Foundation of China (91016004, 61273152, 61203041, 61127007), and Natural Science Foundation of Shandong Province (ZR2011FM0 17, ZR2013FL007)

摘要

摘要: 复杂工作环境中，许多自然现象的个体动力学特性用整数阶方程不能描述，只能用非整数阶（分数阶）动力学来描述个体的运动行为. 本文假设多自主体系统内部连接组成有向加权网络，个体的动态特性应用分数阶动力学方程描述，个体之间数据传输存在通信时延. 应用分数阶系统的Laplace变换和频域理论，研究了离散时间的分数阶多自主体系统的渐近一致性. 应用Hermit-Biehler 定理，研究了具有样本时延的分数阶多自主体系统的运动一致性，得到保证系统稳定的时延的上界阈值. 最后应用一个实例对结论进行了验证.
- 多自主体系统 /
- 分数阶 /
- 离散时间 /
- 样本时延 /
- 一致性
Abstract: In the complex practical environments, many distributed multi-agent systems can not be described with the integer-order dynamics and can only be illustrated with the fractional-order dynamics. In this paper, consensus problems of discrete-time networked fractional-order multi-agent systems with sampling delay are investigated. Firstly, the collaborative control of discrete-time multi-agent systems with fractional-order operator is analyzed in a directed network ignoring sampling delay by using Laplace transform and frequency domain. Then, by applying Hermit-Biehler theorem, the consensus of fractional-order multi-agent systems with sampling delay is studied in a misdirected network. A number of consensus conditions for fractional-order systems with sampling delay are obtained. Numerical simulations are shown to illustrate the utility of the theoretical results.
- Multi-agent systems /
- fractional-order /
- discrete time /
- sampling delay /
- consensus

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参考文献(27)

[1]	Reynolds C W. Flocks, herds, and schools: a distributed behavioral model. Computer Graphics, 1987, 21(4): 25-34
[2]	Vicsek T, Cziroo'k A, Ben-Jacob E, Cohen I, Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letter, 1995, 75(6): 1226-1229
[3]	Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001
[4]	Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533
[5]	Ren W, Beard R W, Atkins E M. Information consensus in multivehicle cooperative control: collective group behavior through local interaction. IEEE Control Systems Magazine, 2007, 27(2): 71-82
[6]	Li S H, Du H B, Lin X Z. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica, 2011, 47(8): 1706-1712
[7]	Yang H Y, Zhang Z X, Zhang S Y. Consensus of second-order multi-agent systems with exogenous disturbances. International Journal of Robust and Nonlinear Control, 2011, 21(9): 945-956
[8]	Meng Z Y, Zhao Z Y, Lin Z L. On global leader-following consensus of identical linear dynamic systems subject to actuator saturation. Systems and Control Letters, 2013, 62(2): 132-142
[9]	Wang Fei-Yue. Parallel control: a method for data-driven and computational control. Acta Automatica Sinica, 2013, 39(4): 293-302(王飞跃. 平行控制: 数据驱动的计算控制方法. 自动化学报, 2013, 39(4): 293-302)
[10]	Chen Guan-Rong. Problems and challenges in control theory under complex dynamical network environments. Acta Automatica Sinica, 2013, 39(4): 312-321(陈关荣. 复杂动态网络环境下控制理论遇到的问题与挑战. 自动化学报, 2013, 39(4): 312-321)
[11]	Yan Jing, Guan Xin-Ping, Luo Xiao-Yuan, Yang Xian. Consensus and trajectory planning with input constraints for multi-agent systems. Acta Automatica Sinica, 2012, 38(7): 1074-1082(闫敬, 关新平, 罗小元, 杨晛. 多智能体系统输入约束下的一致性与轨迹规划研究. 自动化学报, 2012, 38(7): 1074-1082)
[12]	Podlubny I. Fractional Differential Equations. San Diego, CA: Academic Press, 1999.
[13]	Torvik P J, Bagley R L. On the appearance of the fractional derivative in the behavior of real material. Journal of Applied Mechanics, Transaction of the ASMF, 1984, 51(2): 294-298
[14]	Ren Wei, Cao Y C. Distributed Coordination of Multi-Agent Networks. London: Springer-Verlag, 2011.
[15]	Cao Y C, Li Y, Ren W, Chen Y Q. Distributed coordination of networked fractional-order systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40(2): 362-370
[16]	Cao Y C, Ren W. Distributed coordination for fractional-order systems: dynamic interaction and absolute/relative damping. Systems and Control Letters, 2010, 43(3-4): 233-240
[17]	Yang Hong-Yong, Guo Lei, Zhang Yu-Ling, Yao Xiu-Ming. Movement consensus of complex fractional-order multi-agent systems. Acta Automatica Sinica, 2014, 40(3): 489-496(杨洪勇, 郭雷, 张玉玲, 姚秀明. 复杂分数阶多自主体系统的运动一致性. 自动化学报, 2014, 40(3): 489-496)
[18]	Tian Y P, Liu C L. Consensus of multi-agent systems with diverse input and communication delays. IEEE Transactions on Automatic Control, 2008, 53(9): 2122-2128
[19]	Cao Y C, Ren W, Li Y. Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication. Automatica, 2009, 45(5): 1299-1305
[20]	Zhao H Y, Ren W, Xu S Y, Yuan D M. Distributed discrete-time coordinated tracking with Markovian switching topologies. Systems and Control Letters, 2012, 61(7): 766-772
[21]	Lin P, Jia Y M. Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica, 2009, 45(9): 2154-2158
[22]	Yu W W, Zheng W X, Cheng G R, Ren W, Cao J D. Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica, 2011, 47: 1496-1503
[23]	Yu J Y, Wang L. Group consensus in multi-agent systems with switching topologies and communication delays. Systems and Control Letters, 59(6): 340-348
[24]	Tian Y P, Liu C L. Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations. Automatica, 2009, 45(5): 1374-1353
[25]	Yang H Y, Zhu X L, Zhang S Y. Consensus of second-order delayed multi-agent systems with leader-following. European Journal of Control, 2010, 16(2): 188-199
[26]	Liu C L, Liu F. Stationary consensus of heterogeneous multi-agent systems with bounded communication delays. Automatica, 2011, 47(9): 2130-2133
[27]	Ogata K. Discrete-Time Control System. Englewood Cliffs, NJ: Prentice-Hall, 1995.