有领导者线性多智能体系统一致性的分析与设计
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摘要
研究有向信息拓扑下有领导者线性多智能体系统的一致性分析与设计问题。利用提出的线性变换,将领导者有扰动输入的多智能体系统一致性问题转换为输入到状态稳定性问题。得到有向信息拓扑下有领导者线性多智能体系统达到一致的基于矩阵Hurwitz稳定的判据和误差估计函数,同时设计反馈增益矩阵,并将有领导者多智能体系统的一致性问题扩展到编队控制问题。数值实例验证表明:所得理论具有有效性。
Consensus analysis and design problem for leader-following linear multi-agent systems(LLMASs) with directed information topology was investigated. A proper linear transformation was proposed to transform the consensus problem of a leader with disturbance inputs to the input-to-state stability problem of a corresponding linear system. Then, a new consensus criterion in terms of Hurwitz stability of matrices was given for LLMASs achieving consensus with directed information topologies, and the tracking error was estimated. Moreover, a design process to determine the feedback gain matrix in the consensus protocol was proposed. Finally, the consensus was extended to the formation control. Numerical examples are given to validate the above theoretical results.
Consensus analysis and design problem for leader-following linear multi-agent systems(LLMASs) with directed information topology was investigated. A proper linear transformation was proposed to transform the consensus problem of a leader with disturbance inputs to the input-to-state stability problem of a corresponding linear system. Then, a new consensus criterion in terms of Hurwitz stability of matrices was given for LLMASs achieving consensus with directed information topologies, and the tracking error was estimated. Moreover, a design process to determine the feedback gain matrix in the consensus protocol was proposed. Finally, the consensus was extended to the formation control. Numerical examples are given to validate the above theoretical results.
引文
[1]OLFATI-SABER R,FAX J A,MURRAY R M.Consensus and cooperation in networked multi-agent systems[J].Proceedings of the IEEE,2007,95(1):215-233.
[2]SUN Yuangong,WANG Long,XIE Guangming.Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays[J].Systems&Control Letters,2008,57(2):175-183.
[3]谭拂晓,关新平,刘德荣.非平衡拓扑结构的多智能体网络系统一致性协议[J].控制理论与应用,2009,26(10):1087-1092.TAN Fuxiao,GUAN Xinping,LIU Derong.Consensus protocol in networked multi-agent systems with non-balanced topology[J].Control Theory&Applications,2009,26(10):1087-1092.
[4]XI Jianxiang,CAI Ning,ZHONG Yisheng.Consensus problems for high-order linear time-invariant swarm systems[J].Physica A:Statistical Mechanics and its Applications,2010,389(24):5619-5627.
[5]MA Cuiqin,ZHANG Jifeng.Necessary and sufficient conditions for consensusability of linear multi-agent systems[J].IEEE Transactions on Automatic Control,2010,55(5):1263-1268.
[6]CHEN Yangzhou,GE Yanrong,ZHANG Yaxiao.Partial stability approach to consensus problem of linear multi-agent systems[J].Acta Automatica Sinica,2014,40(11):2573-2584.
[7]REN Wei.Consensus tracking under directed interaction topologies:algorithms and experiments[J].IEEE Transactions on Control Systems Technology,2010,18(1):230-237.
[8]HONG Yiguang,HU Jiangping,GAO Linxin.Tracking control for multi-agent consensus with an active leader and variable topology[J].Automatica,2006,42(7):1177-1182.
[9]PENG Ke,YANG Yupu.Leader-following consensus problem with a varying-velocity leader and time-varying delays[J].Physica A:Statistical Mechanics and its Applications,2009,388(2/3):193-208.
[10]MA Cuiqin,LI Tao,ZHANG Jifeng.Consensus control for leader-following multi-agent systems with measurement[J].Journal of Systems Science and Complexity,2010,23(1):35-49.
[11]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.
[12]SONG Qiang,CAO Jinde,YU Wenwu.Second-order leader-following consensus of nonlinear multi-agent systems via pinning control[J].Systems&Control Letters,2010,59(9):553-562.
[13]HU Guoqiang.Robust consensus tracking of a class of second-order multiagent dynamic systems[J].Systems&Control Letters,2012,61(1):134-142.
[14]ZHU Wei,CHENG Daizhan.Leader-following consensus of second-order agents with multiple time-varying delays[J].Automatica,2010,46(12):1994-1999.
[15]JIANG Fangcui,WANG Long.Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies[J].International Journal of Control,2010,83(2):404-420.
[16]NI Wei,CHENG Daizhan.Leader-following consensus of multi-agent systems under fixed and switching topologies[J].Systems&Control Letters,2010,59(3/4):209-217.
[17]NI Wei,XIONG Chun,YANG Jie.Leader-following consensus of high-order multi-agent linear systems with bounded transmission channels[J].International Journal of Systems Science,2013,44(9):1711-1725.
[18]TANNER H G,PAPPAS G J,KUMAR V.Input-to-state stability on formation graphs[C]//Proceedings of the 41st IEEE Conference on Decision and Control,NJ:IEEE,2002:2439-2444.
[19]KHALIL H K,GRIZZLE J W.Nonlinear systems[M].3rd ed.Upper Saddle River:Prentice Hall,2002:174-180.
[20]HORN R A,JOHNSON C R.Topics in matrix analysis[M].Cambridge,UK:Cambridge University Press,1991:242-254.
[2]SUN Yuangong,WANG Long,XIE Guangming.Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays[J].Systems&Control Letters,2008,57(2):175-183.
[3]谭拂晓,关新平,刘德荣.非平衡拓扑结构的多智能体网络系统一致性协议[J].控制理论与应用,2009,26(10):1087-1092.TAN Fuxiao,GUAN Xinping,LIU Derong.Consensus protocol in networked multi-agent systems with non-balanced topology[J].Control Theory&Applications,2009,26(10):1087-1092.
[4]XI Jianxiang,CAI Ning,ZHONG Yisheng.Consensus problems for high-order linear time-invariant swarm systems[J].Physica A:Statistical Mechanics and its Applications,2010,389(24):5619-5627.
[5]MA Cuiqin,ZHANG Jifeng.Necessary and sufficient conditions for consensusability of linear multi-agent systems[J].IEEE Transactions on Automatic Control,2010,55(5):1263-1268.
[6]CHEN Yangzhou,GE Yanrong,ZHANG Yaxiao.Partial stability approach to consensus problem of linear multi-agent systems[J].Acta Automatica Sinica,2014,40(11):2573-2584.
[7]REN Wei.Consensus tracking under directed interaction topologies:algorithms and experiments[J].IEEE Transactions on Control Systems Technology,2010,18(1):230-237.
[8]HONG Yiguang,HU Jiangping,GAO Linxin.Tracking control for multi-agent consensus with an active leader and variable topology[J].Automatica,2006,42(7):1177-1182.
[9]PENG Ke,YANG Yupu.Leader-following consensus problem with a varying-velocity leader and time-varying delays[J].Physica A:Statistical Mechanics and its Applications,2009,388(2/3):193-208.
[10]MA Cuiqin,LI Tao,ZHANG Jifeng.Consensus control for leader-following multi-agent systems with measurement[J].Journal of Systems Science and Complexity,2010,23(1):35-49.
[11]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.
[12]SONG Qiang,CAO Jinde,YU Wenwu.Second-order leader-following consensus of nonlinear multi-agent systems via pinning control[J].Systems&Control Letters,2010,59(9):553-562.
[13]HU Guoqiang.Robust consensus tracking of a class of second-order multiagent dynamic systems[J].Systems&Control Letters,2012,61(1):134-142.
[14]ZHU Wei,CHENG Daizhan.Leader-following consensus of second-order agents with multiple time-varying delays[J].Automatica,2010,46(12):1994-1999.
[15]JIANG Fangcui,WANG Long.Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies[J].International Journal of Control,2010,83(2):404-420.
[16]NI Wei,CHENG Daizhan.Leader-following consensus of multi-agent systems under fixed and switching topologies[J].Systems&Control Letters,2010,59(3/4):209-217.
[17]NI Wei,XIONG Chun,YANG Jie.Leader-following consensus of high-order multi-agent linear systems with bounded transmission channels[J].International Journal of Systems Science,2013,44(9):1711-1725.
[18]TANNER H G,PAPPAS G J,KUMAR V.Input-to-state stability on formation graphs[C]//Proceedings of the 41st IEEE Conference on Decision and Control,NJ:IEEE,2002:2439-2444.
[19]KHALIL H K,GRIZZLE J W.Nonlinear systems[M].3rd ed.Upper Saddle River:Prentice Hall,2002:174-180.
[20]HORN R A,JOHNSON C R.Topics in matrix analysis[M].Cambridge,UK:Cambridge University Press,1991:242-254.