离散线性一致性算法噪声问题研究

窦全胜; 丛玲; 姜平; 史忠植

doi:10.16383/j.aas.2015.c140698

离散线性一致性算法噪声问题研究

doi: 10.16383/j.aas.2015.c140698

窦全胜^1,2,3,
丛玲^1,2,
姜平^1,2,
史忠植³

1.
山东工商学院计算机与技术学院烟台 264005;
2.
山东省高校智能信息处理重点实验室(山东工商学院) 烟台 264005;
3.
中国科学院计算技术研究所北京 100190

基金项目:

图家重点基础研究发展计划(973计划) (2013CB329502),国家自然科学基金(61272244, 611750532, 61173173, 61035003, 61202212)资助

详细信息

作者简介:
丛玲山东师范大学信息科学与工程学院硕士研究生. 主要研究方向为群体智能. E-mail: clfighting@sina.com

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出版历程
- 收稿日期: 2014-10-09
- 修回日期: 2015-02-02
- 刊出日期: 2015-07-20

Research on Discrete Linear Consensus Algorithm with Noises

1.
School of Computer Science and Technology, Shandong Institute of Business and Technology, Yantai 264005;
2.
Key Laboratory of Intelligent Information Processing in Universities of Shandong, Yantai 264005;
3.
Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190

Funds:

Supported by National Basic Research Program of China (973 Program) (2013CB329502) and National Natural Science Foundation of China (61272244, 611750532, 61173173, 61035003, 612 02212)

摘要

摘要: 多智能体一致性问题在传感网、社交网、协同控制等诸多领域有着广泛的实际应用背景, 本文对离散线性一致性算法的噪声问题进行了研究, 证明了离散线性一致性算法的噪声不可控性; 提出基于抑噪算子ε(t)的噪声控制策略, 指出当ε(t)为t-0.5的高阶无穷小时, 抑噪后的一致性算法噪声可控; 分析了抑噪算子对一致性算法收敛性的影响, 证明了在无噪声条件下, 当抑噪算子ε(t为t-1的低阶无穷小时, 抑噪后的一致性算法依然可以使Agent收敛至原收敛状态x*.在上述结论基础上进一步指出, 当t→∞ 时, 若抑噪算子ε(t)的阶在t-0.5~t-1之间, 所有Agent 的状态将以原收敛状态x* 为中心呈正态分布. 最后, 以DHA 为例对相应理论结果进行了验证和讨论. 本文为线性一致性算法的噪声控制提供了理论依据, 对抑噪算s子的确定有较强的指导意义.
- 集群智能 /
- 多智能体系统 /
- 一致性算法 /
- 噪声
Abstract: Consensus problem in multi-agent system has a wide application background in many fields, such as sensor networks, social networks, cooperative control and so on. In this paper, we address the problem of the discrete linear consensus algorithm with noise, and point out that the noise of discrete linear consistency algorithm is not controllable. Aiming at this problem, we propose a strategy using noise suppression operator ε(t) to control noise, and point out that when ε(t) is the higher-order infinitesimal of t-0.5, the noise of consistency algorithm after noise suppression is controllable. We analyze the effect of suppression operator on the convergence of consistency algorithm and prove that under the condition of no noise and if the suppression operator ε(t) is a lower-order infinitesimal of t-1, the consistency algorithm after noise suppression can still converge to the original convergence state x*. Based on this, we further point out that if the order of ε(t is between the orders of t-0.5 and t-1 when t→∞,the states of all the agents will be a normal distribution with its center at the original convergence state x* in the end. And, by using DHA as an example, we verify and discuss the corresponding theoretical results. This paper provides a theoretical foundation for noise control of linear consensus algorithm, and has a strong directional effect on the determination of noise suppression operator.
- Collective intelligence /
- multi-agents system /
- consensus algorithms /
- noises

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