基于LMS的多智能体系统变步长自调优一致性
Variable Step Self-Tuning Consensus of Multi-Agent Systems with Least Mean Squares Method
DOI: 10.12677/CSA.2018.86097, PDF,   
作者: 韩宗亭*, 吴宪祥, 呼香艳, 郭宝龙, 陈 曦：西安电子科技大学空间科学与技术学院，陕西 西安
关键词: 多智能体系统；一致性；自调优；最小均方算法；Multi-Agent Systems； Consensus； Self-Tuning； Least Mean Squares Method
摘要: 研究了离散时间多智能体系统中的一致性问题。在不使用任何全局信息的情况下，将粒子群的变步长算法应用到最小均方(LMS)算法中进行多智能体局部自调，实现了多智能体的一致性。在这个过程中，网络模型的代价函数取决于智能体的状态和邻居状态平均值之间的误差。同时证明了网络图强连通的情况下，所有的智能体状态将达到一致性。最后，通过在不同拓扑结构下的仿真实例对提出的算法进行验证。
Abstract: This paper considers the consensus problem in discrete time multi-agent systems. By using variable step particle swarm algorithm, the coupling parameters among agents are locally self-tuned by least-mean square (LMS) algorithm, without using any global information. In this process, each agent minimizes a local cost function dependent on the error between the agent state and the average of neighbors’ states. Provided that the network graph is strongly connected, it is shown that for each agent, the sequence of coupling parameters is convergent, and all agent states converge toward the same constant value. Finally, the proposed algorithm is verified by simulation under different topologies.
文章引用：韩宗亭, 吴宪祥, 呼香艳, 郭宝龙, 陈曦. 基于LMS的多智能体系统变步长自调优一致性[J]. 计算机科学与应用, 2018, 8(6): 877-887. https://doi.org/10.12677/CSA.2018.86097

参考文献

[1] [1] Olfati-Saber, R. and Murray, R.M. (2004) Consensus Problems in Networks of Agents with Switching Topology and Time-Delays. IEEE Transactions on Automatic Control, 49, 1520-1533. [Google Scholar] [CrossRef] 
[2] Ren, W. and Beard, R.W. (2005) Consensus Seeking in Mul-ti-Agent Systems under Dynamically Changing Interaction Topologies. IEEE Transactions on Automatic Control, 50, 655-661. [Google Scholar] [CrossRef] 
[3] 李静, 方正. 分数阶非线性多智能体系统的一致性研究[J]. 计算机工程与应用, 2016, 52(23): 63-67.
[4] Li, T. and Zhang. J.F. (2010) Consensus Conditions of Mul-ti-Agent Systems with Time-Varying Topologies and Stochastic Communication Noises. IEEE Transactions on Auto-matic Control, 55, 2043-2057. [Google Scholar] [CrossRef] 
[5] Dong, X.W., Xi, J.X., Shi, Z.Y., et al. (2013) Practical Consen-sus for High-Order Linear Time-Invariant Swarm Systems with Interaction Uncertainties, Time-Varying Delays and Ex-ternal Disturbances. International Journal of Systems Science, 44, 1843-1856. [Google Scholar] [CrossRef] 
[6] Jadbabaie, A., Lin, J. and Morse, A.S. (2003) Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules. IEEE Transactions on Automatic Control, 48, 988-1001. [Google Scholar] [CrossRef] 
[7] 王品, 姚佩阳. 具有不同输入时延的二阶多智能体系统一致性[J]. 复杂系统与复杂性科学, 2016, 13(4): 102-107.
[8] Bai, H., Arcak, M. and Wen, J. (2011) Coopera-tive Control Design: A Systematic-Passivity Based Approach. Springer-Verlag, New York. [Google Scholar] [CrossRef] 
[9] Ma, T.D., Zhang, L.Y. and Gu, Z.Y. (2016) Further Studies on Impulsive Consensus of Multi-Agent Nonlinear Systems with Control Gain Error. Neurocomputing, 190, 140-146. [Google Scholar] [CrossRef] 
[10] 袁玩贵, 屈百达. 受干预多智能体系统的一致性分析及控制[J]. 控制与决策, 2016, 31(1): 187-192.
[11] Cao, Y., Yu, W., Ren, W. and Chen, G. (2013) An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination. IEEE Transactions on Industrial Informatics, 9, 427-438. [Google Scholar] [CrossRef] 
[12] Zhou, J., Lu, J. and Lü, J. (2006) Adaptive Synchronization of an Uncertain Complex Dynamical Network. IEEE Transactions on Automatic Control, 51, 652-656. [Google Scholar] [CrossRef] 
[13] Zhou, J., Lu, J. and Lü, J. (2008) Pinning Adaptive Synchroniza-tion of a General Complex Dynamical Network. Automatica, 44, 996-1003. [Google Scholar] [CrossRef] 
[14] DeLellis, P., diBernardo, M. and Garofalo, F. (2009) Novel Decentralized Adaptive Strategies for Synchronization of Complex Networks. Automatica, 45, 1312-1318. [Google Scholar] [CrossRef] 
[15] Das, A. and Lewis, F. (2010) Distributed Adaptive Control for Synchronization of Unknown Nonlinear Networked Systems. Automatica, 46, 2014-2021. [Google Scholar] [CrossRef] 
[16] Yu, H. and Xia, X. (2012) Adaptive Consensus for Mul-ti-Agents in Networks with Jointly Connected Topologies. Automatica, 48, 1783-1790. [Google Scholar] [CrossRef] 
[17] Li, Z., Ren, W., Liu, X. and Xie, L. (2013) Distributed Con-sensus of Linear Multi-Agent Systems with Adaptive Dynamic Protocols. Automatica, 49, 1986-1995. [Google Scholar] [CrossRef] 
[18] Radenkovic, M. and Bose, T. (2015) On Multi-Agent Self-Tuning Consensus. Pergamon Press, Inc., Oxford.
[19] 张清华. 图论及其应用[M]. 北京: 清华大学出版社, 2013: 2-4.
[20] 吴永红, 刘敬贤. 多智能体网络一致性协同控制理论及应用[M]. 北京: 科学出版社, 2013.
[21] 李霄剑, 王永, 陈绍青, 等. 一种方向优化最小均方算法[J]. 电子与信息学报, 2014, 36(6): 1348-1354.