线性均方一致性问题的偏差估计

窦全胜; 刘柏枫; 厉玉蓉; 史忠植

doi:10.16383/j.aas.2017.c160064

线性均方一致性问题的偏差估计

doi: 10.16383/j.aas.2017.c160064

窦全胜^1,2, ,,
刘柏枫^3,,
厉玉蓉^1,,
史忠植^4,

1.
山东工商学院计算机与技术学院烟台 264005
2.
山东省车联网工程技术中心烟台 264005
3.
山东工商学院数学与信息科学学院烟台 264005
4.
中国科学院计算技术研究所北京 100190

基金项目:

国家自然科学基金 61035003

国家自然科学基金 61202212

国家自然科学基金 61175053

国家自然科学基金 61173173

国家重点基础研究发展计划（973计划） 2013CB329502

国家自然科学基金 71471103

国家自然科学基金 61272244

详细信息

作者简介:
刘柏枫博士, 山东工商学院数学与信息科学学院副教授.主要研究方向为随机过程, 微分方程动力系统.E-mail:lbfg@sohu.com

厉玉蓉博士, 山东工商学院计算机与技术学院教授.主要研究方向为计算机代数, 计算机图形学.E-mail:lyry@263.net

史忠植中国科学院计算技术研究所研究员.主要研究方向为智能科学理论与方法, 知识工程, 神经计算, 数据挖掘, 机器学习.E-mail:shizz@ics.ict.ac.cn

通讯作者:
窦全胜博士, 山东工商学院计算机与技术学院教授.主要研究方向为智能科学理论与方法, 数据挖掘, 多主体技术, 群体智能.E-mail:lidou@163.com

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出版历程
- 收稿日期: 2016-01-22
- 录用日期: 2016-05-16
- 刊出日期: 2017-04-20

Variance Estimation for Linear Mean Square Consensus Problem

1.
School of Computer Science and Technology, Shandong Institute of Business and Technology, Yantai 264005
2.
Shandong Vehicle Networking Engineering Technology Research Center, Yantai 264005
3.
College of Mathematic and Information Science, Shandong Institute of Business and Technology, Yantai 264005
4.
Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190

Funds:

National Natural Science Foundation of China 61035003

National Natural Science Foundation of China 61202212

National Natural Science Foundation of China 61175053

National Natural Science Foundation of China 61173173

National Basic Research Program of China (973 Program) 2013CB329502

National Natural Science Foundation of China 71471103

National Natural Science Foundation of China 61272244

More Information

Author Bio:
Ph. D., associate professor at the College of Mathematic and Information Science, Shandong Inresearch interest covers stochastic process and differential equation dynamic system

Ph. D., professor at the School of Computer Science and Technology, Shandong Institute of Business and Technology. Her research interest covers computer algebra and computer graphics

Professor at the Institute of Computing Technology, Chinese Academy of Sciences. His research interest covers intelligent scientific theory and method, knowledge engineering, neural computing, data mining, and machine learning

Corresponding author: DOU Quan-Sheng Ph. D., professor at the School of Computer Science and Technology, Shandong Institute of Business and Technology. His research interest covers intelligent scientific theory and method, data mining, multi-agent technology, and swarm intelligence. Corresponding author of this paper

摘要

摘要: 多智能体协同在传感网、社交网、分布式控制等诸多领域有着广泛的实际应用背景，一致性问题作为多智能体协同的基础，受到越来越多研究者的关注.在实际环境中，由于设备、通信干扰等诸多原因，信息在传递过程中通常会携有噪声，本文对噪声条件下一致性问题的系统偏差进行了研究，将求解一致性协议噪声偏差问题转化成矩阵范数的积分问题，根据矩阵迹与特征值的关系，利用范数不等式及积分中值定理，给出仅与增益函数和网络结构相关的一致性协议噪声偏差上界，为一致性系统在实际应用中的噪声估计奠定了理论基础.
- 集群智能 /
- 多智能体系统 /
- 一致性协议 /
- 均方一致
Abstract: Multi-agent cooperation has found applications in many fields such as sensor network, social network, distributed control, etc. The consistency problem is the basis for multi-agent cooperation, and receives much attention from more and more researchers. In real circumstances, because of equipment and communication interference, the information often carries noise during the transfer process. The paper studies the system deviation of consistency problem under noise condition, and the solution of noise deviation problem under consistency protocol is transformed into the integral of matrix norm. According to the relationship of trace and eigenvalue of the matrix, and based on the norm inequation and mean value theorem of integrals, the upper bound of noise deviation under consistency protocol which is only related with gain function and network structure is given, which establishes a theoretical basis for noise evaluation of consistent systems in real application.
- Collective intelligence /
- multi-agents system /
- consensus protocol /
- mean square consensus
注释:

1) 本文责任编委吕金虎

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图 1 四种Agent网络结构示意图

Fig. 1 Diagram of four different network structures of Agent

下载: 全尺寸图片幻灯片

图 2 有两个邻居时Agent的结构

Fig. 2 Structure of Agent with two neighbors

下载: 全尺寸图片幻灯片

图 3 $Z(t)$ 理论上界与统计结果对比

Fig. 3 The Comparison of theoretical upper bound and statistical results of $Z(t)$

下载: 全尺寸图片幻灯片

表 1 L_star所有非零特征值

Table 1 All nonzero eigenvalues of L_star

λ_i (L_star)
i = 2	i = 3	i = 4	i = 5	i = 6	i = 7	i = 8
1.00	1.00	1.00	1.00	1.00	1.00	8.00

下载: 导出CSV

表 2 L_path所有非零特征值

Table 2 All nonzero eigenvalues of L_path

λ_i (L_path)
i = 2	i = 3	i = 4	i = 5	i = 6	i = 7	i = 8
0.152	0.586	1.235	2.000	2.765	3.414	3.848

下载: 导出CSV

表 3 L_circle所有非零特征值

Table 3 All nonzero eigenvalues of L_circle

λ_i (L_circle)
i = 2	i = 3	i = 4	i = 5	i = 6	i = 7	i = 8
0.586	0.586	2.000	2.000	3.414	3.414	4.000

下载: 导出CSV

表 4 L_{circle_N4}所有非零特征值

Table 4 All nonzero eigenvalues of L_{circle_N4}

λ_i (L_{circle_N4})
i = 2	i = 3	i = 4	i = 5	i = 6	i = 7	i = 8
2.586	2.586	4.000	5.414	5.414	6.000	6.000

下载: 导出CSV

表 5 Z(t) 理论上界与统计值的数据对比

Table 5 The detailed comparison of theoretical upper bound and statistical results of Z(t)

网络结构	Star	Path	Circle	Circle_N4
Z(t)理论上界	42.875	73.512	41.999	27.619
Z(t)统计值	33.856	59.689	30.518	22.335

下载: 导出CSV

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