logo

SCIENTIA SINICA Informationis, Volume 46, Issue 11: 1621-1632(2016) https://doi.org/10.1360/N112016-00140

Mean-square consensus of heterogeneous multi-agent systemsunder Markov switching topologies

More info
  • ReceivedAug 25, 2016
  • AcceptedOct 26, 2016
  • PublishedNov 9, 2016

Abstract

This paper concerns the mean-square consensus of a heterogeneous multi-agent system, which consists of first- and second-order agents, under Markovian switching topologies. Firstly, based on information from neighboring agents, control protocols are designed for the first- and second-order agents, respectively. Secondly, by using the properties of a stochastic irreducible aperiodic matrix, the sufficient and necessary conditions for the heterogeneous multi-agent systems to realize mean-square consensus are obtained. Finally, numerical simulations are conducted to illustrate the effectiveness of the theoretical results.


Funded by

国家自然科学基金(61304155)

北京市组织部优秀人才项目(2012D005003000005)


References

[1] Vicsek T, Czirók A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles. Phys Rev Lett, 1995, 75: 1226-1229 CrossRef Google Scholar

[2] Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor. IEEE Trans Autom Contr, 2003, 48: 988-1001 CrossRef Google Scholar

[3] Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Contr, 2004, 49: 1520-1533 CrossRef Google Scholar

[4] Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Contr, 2005, 50: 655-661 CrossRef Google Scholar

[5] Lin P, Jia Y M, Li L. Distributed robust $H_\infty$ consensus control in directed networks of agents with time-delay. Syst Contr Lett, 2008, 57: 643-653 CrossRef Google Scholar

[6] Zhang W G, Qu S. Leader-following multi-agent consensus control. J Astronaut, 2010, 31: 2172-2176. Google Scholar

[7] Li T, Zhang J. Sampled-data based average consensus control for networks of continuous-time integrator agents with measurement noises. In: Proceedings of the 26th Chinese Control Conference. Beijing: Beihang University Press, 2007. 716-720. Google Scholar

[8] Li T, Zhang J F. Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica, 2009, 45: 1929-1936 CrossRef Google Scholar

[9] Li T, Zhang J F. Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle. Sci China Inf Sci, 2009, 52: 2089-2103 CrossRef Google Scholar

[10] Cheng L, Hou Z G, Tan M. A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies. IEEE Trans Autom Contr, 2014, 59: 261-267 CrossRef Google Scholar

[11] Zheng Y, Zhu Y, Wang L. Consensus of heterogeneous multi-agent systems. IET Contr Theory Appl, 2011, 5: 1881-1888 CrossRef Google Scholar

[12] Liu C L, Liu F. Stationary consensus of heterogeneous multi-agent systems with bounded communication delays. Automatica, 2011, 47: 2130-2133 CrossRef Google Scholar

[13] Zheng Y, Wang L. Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. Int J Contr, 2012, 85: 1967-1976 CrossRef Google Scholar

[14] Zheng Y, Wang L. Containment control of heterogeneous multi-agent system. Int J Contr, 2014, 87: 1-8 CrossRef Google Scholar

[15] Haghshenas H, Badamchizadeh M A, Baradarannia M. Containment control of heterogeneous linear multi-agent systems. Automatica, 2015, 54: 210-216 CrossRef Google Scholar

[16] Liu Y, Min H, Wang S, et al. Distributed consensus of a class of networked heterogeneous multi-agent systems. J Franklin Inst, 2014, 351: 1700-1716 CrossRef Google Scholar

[17] Liu K, Ji Z, Xie G, et al. Consensus for heterogeneous multi-agent systems under fixed and switching topologies. J Franklin Inst, 2015, 352: 3670-3683 CrossRef Google Scholar

[18] Geng H, Chen Z, Liu Z, et al. Consensus of a heterogeneous multi-agent system with input saturation. Neurocomputing, 2015, 166: 382-388 CrossRef Google Scholar

[19] Mo L, Pan T, Guo S, et al. Distributed coordination control of first- and second-order multiagent systems with external disturbances. Math Problems Eng, 2015, 9: 1-7. Google Scholar

[20] Mo L, Niu Y, Pan T. Consensus of heterogeneous multi-agent systems with switching jointly-connected interconnection. Phys A: Stat Mech Appl, 2015, 427: 132-140 CrossRef Google Scholar

[21] Tian Y, Zhang Y. High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica, 2012, 48: 1205-1212. Google Scholar

[22] Zhang Y, Tian Y. Consentability and protocol design of multi-agent systems with stochastic switching topology. Automatica, 2009, 45: 1195-1201 CrossRef Google Scholar

[23] Wang B, Zhang J. Distributed output feedback control of Markov jump multi-agent systems. Automatica, 2013, 49: 1397-1402 CrossRef Google Scholar

[24] Miao G, Li T. Mean square containment control problems of multi-agent systems under Markov switching topologies. Adv Differ Equ, 2015, 1: 1-10. Google Scholar

[25] Xie D, Cheng Y. Bounded consensus tracking for sampled-data second-order multi-agent systems with fixed and Markovian switching topology. Int J Robust Nonlin Contr, 2013, 25: 252-268. Google Scholar

[26] Lou Y C, Hong Y G. Target containment control of multi-agent systems with random switching interconnection topologies. Automatica, 2012, 48: 879-885 CrossRef Google Scholar

[27] Wolfowitz J. Products of indecomposable, aperiodic, stochastic matrices. Proc American Math Soc, 1963, 14: 733-737 CrossRef Google Scholar

[28] He S Y. Stochastic Process. Beijing: Beijing University Press, 2008. 145-173 [何书元. 随机过程. 北京: 北京大学出版社, 2008. 145-173]. Google Scholar

[29] Xu Z. Introduction to Matrix Theory. Beijing: Science Press, 2001. 158-162 [徐仲. 矩阵论简明教程. 北京: 科学出版社, 2001. 158-162]. Google Scholar

[30] Costa O L V, Fragoso M D, Marques R P. Discrete-Time Markov Jump Linear Systems. London: Springer-Verlag, 2005. 63-66. Google Scholar

[31] Kim J M, Jin B P, Choi Y H. Leaderless and leader-following consensus for heterogeneous multi-agent systems with random link failures. IET Contr Theory Appl, 2014, 8: 51-60 CrossRef Google Scholar

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1