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Convergence of a class of multi-agent systems in probabilistic framework
  • 时间：0
  • 分类：TP273[自动化与计算机技术—控制科学与工程;自动化与计算机技术—检测技术与自动化装置]
  • 作者机构：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
  • 相关基金：The research is supported by National Natural Science Foundation of China under the Grants No. 60221301 and No. 60334040.Acknowledgement The authors would like to thank Prof. Feng TIAN and Dr. Mei LU for providing the proof of Lemma 6 in Appendix B. We would also like to thank Ms. Zhixin Liu for valuable discussions.
  • 相关项目：控制科学中若干关键基础问题的研究
关键词： 多AGENT系统, 同步, 自动化系统, 大偏差, 局部相互作用, Connectivity, large deviation, local interaction rules, multi-agent systems, random geometric graph, spectral graph theory, synchronization, Vicsek model
中文摘要：

多代理人系统在自然、人工的系统，和一个基本问题从多样的领域产生是理解交往的代理人怎么局部地导致集体行为(例如，同步) 全面系统。在这篇论文，我们将考虑被著名 Vicsek 模型的简化描述的多代理人系统的一个基本的班。这个模型看起来简单，但是严密理论分析是相当复杂的，因为在在模型的代理人之中有强壮的非线性的相互作用。事实上，大多数同步上的存在结果需要在代理人的轨道的全球行为上强加某个连接条件(或在靠近环的动态邻居图上) ，它是相当难的一般来说验证。在这篇论文，由把一个概率的框架介绍给这个问题，只要代理人的数字足够大，我们将为全面多代理人系统将与大概率同步的事实提供一个完全、严密的证明。证明基于非线性的系统进化的动态性质和随机的几何图的光谱的 asymptotic 性质的详细分析。

英文摘要：

Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors （e.g., synchronization） of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents＇ trajectories （or on the closed-loop dynamic neighborhood graphs）, which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs.

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复杂动态系统的建模与控制及其算法实现
期刊论文 14 著作 3
控制科学中若干关键基础问题的研究
期刊论文 189 会议论文 160 获奖 2 著作 7
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