切换信息拓扑和时变时滞下离散时间线性多智能体系统一致性的平均驻留时间条件

盖彦荣; 陈阳舟; 张亚霄

doi:10.3724/SP.J.1004.2014.02609

切换信息拓扑和时变时滞下离散时间线性多智能体系统一致性的平均驻留时间条件

doi: 10.3724/SP.J.1004.2014.02609

1.
北京工业大学电子信息与控制工程学院北京 100124;
2.
河北师范大学物理科学与信息工程学院石家庄 050024

基金项目:

Supported by National Natural Science Foundation of China (61079001, 61273006), National High Technology Research and Development Program of China (863 Program) (2011AA110301), Specialized Research Fund for the Doctoral Program of Higher Education of China (20111103110017), Hebei Province Science and Technology Research and Development Planning Project (10203548D), Hebei Province Science and Technology Planning Project (13210807) Hebei Province Science and Technology Conditions Building Program (11963546D)

计量
- 文章访问数: 1395
- HTML全文浏览量: 65
- PDF下载量: 1002
- 被引次数: 0
出版历程
- 收稿日期: 2013-06-21
- 修回日期: 2013-10-29
- 刊出日期: 2014-11-20

Average Dwell-time Conditions for Consensus of Discrete-time Linear Multi-agent Systems with Switching Topologies and Time-varying Delays

1.
College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China;
2.
College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China

Funds:

摘要

摘要: 研究了有向切换信息拓扑和时变时滞下离散时间线性多智能体系统的一致性问题.首先,通过适当的线性变换把一致性问题转化为相应的时变时滞线性切换系统的渐近稳定问题; 然后,利用构建的李亚普诺夫函数和平均驻留时间模式,建立了一致性问题可解的基于线性矩阵不等式的时滞依赖充分条件,研究了如下两种情形: 1)所有信息拓扑都是可一致的,2) 部分信息拓扑是可一致的; 最后,数值实例验证了结果的正确性.
- 多智能体系统 /
- 一致性 /
- 有向切换信息拓扑 /
- 时变时滞 /
- 平均驻留时间 /
- 线性矩阵不等式
Abstract: This paper investigates the consensus problem of discrete-time linear multi-agent systems (DLMASs) with directed switching information topologies and time-varying delays. First, we transform the consensus problem to an asymptotic stability problem of a corresponding time-delayed switched linear system (TDSLS) via a proper linear transformation. Then by using a constructed Lyapunov functional and the average dwell-time scheme, we establish a novel delay-dependent sufficient condition for the solvability of the consensus problem in terms of linear matrix inequalities (LMIs) for two cases, respectively: 1) all of the given information topologies are consensusable; 2) some of the given information topologies are consensusable. Finally, numerical examples are given to show the validness of the established results.
- Multi-agent systems (MASs) /
- consensus /
- directed switching information topologies /
- time-varying delay /
- average dwelltime /
- linear matrix inequalities (LMIs)

HTML全文

参考文献(32)

[1]	Lynch N A. Distributed Algorithms. San Francisco, CA: Morgan Kaufmann, 1996.
[2]	Chen J, Yu M, Dou L H, Gan M G. A fast averaging synchronization algorithm for clock oscillators in nonlinear dynamical network with arbitrary time-delays. Acta Automatica Sinica, 2010, 36(6): 873-880
[3]	Tsitsiklis J N, Athans M. Convergence and asymptotic agreement in distributed decision problems. IEEE Transactions on Automatic Control, 1984, 29(1): 42-50
[4]	Carli R, Chiuso A, Schensto L, Zampieri S. Distributed Kalman filtering based on consensus strategies. IEEE Journal on Selected Areas in Communications, 2008, 26(4): 622-633
[5]	Serpedin E, Chaudhari Q M. Synchronization in Wireless Sensor Networks: Parameter Estimation, Performance Benchmarks, and Protocols. New York: Cambridge University Press, 2009.
[6]	Olfati-Saber R, Jalalkamali P. Coupled distributed estimation and control for mobile sensor networks. IEEE Transactions on Automatic Control, 2012, 57(10): 2609-2614
[7]	Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 2004, 49(9): 1465-1476
[8]	Ren W. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control, 2008, 53(6): 1503-1509
[9]	Huang Q Z. Consensus analysis of multi-agent discrete-time systems. Acta Automatica Sinica, 2012, 38(7): 1127-1133
[10]	Yan J, Guan X P, Luo X Y, Yang X. Consensus and trajectory planning with input constraints for multi-agent systems. Acta Automatica Sinica, 2012, 38(7): 1074-1082
[11]	Ge Y R, Chen Y Z, Zhang Y X, He Z H. State consensus analysis and design for high-order discrete-time linear multiagent systems. Mathematical Problems in Engineering, 2013, 2013, Article ID 192351
[12]	Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 2005, 50(5): 655-661
[13]	Kingston D B, Beard R W. Discrete-time average-consensus under switching network topologies. In: Proceedings of the 2006 American Control Conference. Minneapolis, Minnesota: IEEE, 2006. 3551-3557
[14]	Xiao F, Wang L. State consensus for multi-agent systems with switching topologies and time-varying delays. International Journal of Control, 2006, 79(10): 1277-1284
[15]	Xiao F, Wang L. Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica, 2008, 44(10): 2577-2582
[16]	Gao Y P, Ma J W, Zuo M, Jiang T Q, Du J P. Consensus of discrete-time second-order agents with time-varying topology and time-varying delays. Journal of the Franklin Institute, 2012, 349(8): 2598-2608
[17]	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
[18]	Su Y F, Huang J. Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica, 2012, 48(9): 1988-1997
[19]	Li Z K, Duan Z H, Chen G R. Consensus of discrete-time linear multi-agent systems with observer-type protocols. Discrete and Continuous Dynamical Systems-Series B, 2011, 16(6): 489-505
[20]	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
[21]	Sun Y G, Wang L, Xie G M. Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. Systems and Control Letters, 2008, 57(2): 175-183
[22]	Jadbabaie A, Lin J, Morse S A. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001
[23]	Liu T, Zhao J, Hill D J. Exponential synchronization of complex delayed dynamical networks with switching topology. IEEE Transactions on Circuits and Systems, 2010, 57(11): 2967-2980
[24]	Chen Y Z, Zhang Y X, He Z H, Ge Y R. Average dwell-time conditions of switching information topologies for consensus of linear multi-agent systems. In: Proceedings of the 32nd Chinese Control Conference, Xi'an, China: IEEE, 2013. 7115-7120
[25]	Hespanha J P, Morse A S. Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE Conference on Decision and Control. Phoenix, Arizona, USA: IEEE, 1999. 2655-2660
[26]	Zhai G S, Hu B, Yasuda K, Michel A N. Qualitative analysis of discrete-time switched systems. In: Proceedings of the American Control Conference. Anchorage, AK: IEEE, 2002. 1880-1885
[27]	Zhang W A, Yu L. Stability analysis for discrete-time switched time-delay systems. Automatica, 2009, 45(10): 2265-2271
[28]	Zhang D, Yu L, Zhang W A. Delay-dependent fault detection for switched linear systems with time-varying delays-the average dwell time approach. Signal Processing, 2011, 91(4): 832-840
[29]	Wu Z G, Shi P, Su H Y, Chu J. Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay. Neurocomputing, 2011, 74(10): 1626-1631
[30]	Horn R A, Johnson C R. Matrix Analysis. Cambridge U. K.: Cambridge University Press, 1987
[31]	Vorotnikov V I. Partial Stability and Control. Basel Berlin: Birkhauser Boston, 1997.
[32]	Gao H J, Chen T W. New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control, 2007, 52(2): 328-334