带有加权的Krause模型的一致性-基础数学专业论文.docxVIP

Classified Index: O175.12 U.D.C: 517.9 Dissertation for the Master Degree in Science ON KRAUSE’S MULTI-AGENT CONSENSUS MOSEL WITH WEIGHT Candidate： Zhang Le Supervisor： Associate Prof. Guo Mengshu Academic Degree Applied for： Master of Science Speciality： Pure Mathematics Affiliation： School of Science Date of Defence： July, 2015 Degree-Conferring-Institution： Harbin Institute of Technology 哈尔滨工业大学理学硕士学位论文 哈尔滨工业大学理学硕士学位论文 I I 摘 要 近年来，多智能体系统（MAS, Multi-Agent System）被广泛研究，多智能体 系统本身具有自主性、协调性和分布性，并有组织能力、学习能力和推理能力。 通常的多智能体模型会假设系统的状态和连接关系可以精确测量和描述的，但是 实际上很多系统内部或者外部的都会有不确定性，尤其是在社会科学领域方面的 问题。例如，绪论中提到的模型都是假定观测值能被精确测量，尤其是观点，都 可以用确定地实数来表示，然而，事实上我们无法精确地测量到一个人的观点的 大小。对于 Cucker-Smale 模型，类似问题也一样存在，因为模型本意是使智能 体根据相对位置决定加速度度的大小，但位置的相对性在实际情形中很难做出精 确评价，标准的 Cucker-Smale 模型反映的只是一种理想状况时的情形而已。为 了能够更加贴近我们的现实情况，有必要加入时变加权来对其进行判定。 本文通过引入时变加权函数来建立 Krause 型模型，进而讨论带有加权的多 智能体模型解的存在性和状态的一致同步性。本文最后也证明在经过一段时间后 任意两个智能体的观点要么会最终收敛到同一种观点，要么它们的观点会永远不 再相互影响，这些结论是和用具体数值建立的 Krause 型模型的结论是一致的。 它是传统模型的扩展和补充。 关键词：Krause 模型；加权函数；解的存在性；一致同步性 II II Abstract In recent years, the multi-agent System (MAS, Multi - Agent System) is widely studied, Multi-agent system has the properties of autonomy, coordination and distribution, and we can use it to HYPERLINK /w/organize/ organize, learn something and ratiocinate. Multi-agent model often assume that the state of the system and the connection relations can accurate measurement and description, but in fact many internal or external system will have uncertainty, especially the problems in the field of social science. For example, mentioned in the introduction, the model is assumed observations can be measured accurately, especially, can be regarded as certainly real numbers. In fact, however, we cannot measure accurately to the size of one’s point of view, for Cucker - Smale model, we also have similar problems. Because the model is intended to make an agent according to the size of the relative position witch is decided by the accelerated speed, but the location of the r