宏观交通流模型的Hopf分叉控制,考虑到车辆制动效应
WenHuan Ai1, MingMing Wang2, DaWei Liu3
1College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730070, Gansu, China. wenhuan618@163.com.
The European physical journal. E, Soft matter
|December 20, 2023
概括
本研究开发了一种随机流量流模型,用于分析和控制交通拥堵. 反控制器旨在通过修改系统分叉特征来防止或减轻拥堵.
科学领域:
- 交通流动动态 交通流动动态
- 分析非线性系统的分析.
- 控制理论 控制理论 控制理论
背景情况:
- 交通拥堵对旅行,能源消耗和空气污染产生重大影响.
- 了解宏观的交通流动模型,特别是车辆制动效应,对于解决交通问题至关重要.
- 现有的模型需要更好地反映出交通流加速和减速的随机性质.
研究的目的:
- 开发一个包含车辆制动和随机行为的随机流量模型.
- 分析Hopf分叉及其在随机流量系统中的控制.
- 设计一个反控制器,通过修改分叉特性来减轻交通拥堵.
主要方法:
- 微宏变量转换为高阶连续流量流量模型.
- 整合一个物理相关的随机函数以建立一个随机流量模型.
- 应用Hopf分叉定理来分析系统稳定性和控制.
- 使用切比舍夫多项式近似来将静态问题转换为确定性的分叉控制问题.
- 设计一个反控制器来管理Hopf分叉和限制周期振幅.
主要成果:
- 在随机流量模型中证明了Hopf分叉的存在.
- 开发了一种方法,将随机问题转化为决定性的分叉控制问题.
- 设计了一个反控制器来延迟Hopf分叉和控制极限周期振幅.
- 通过控制极限周期振幅而不会改变系统的平衡点,可以完全消除霍普夫分叉.
结论:
- 开发的随机流量流量模型准确地反映了不确定的交通行为.
- 反控制器有效地修改系统分叉特征,以防止或减轻交通拥堵.
- 这种方法为管理交通流量和减少拥堵影响提供了一个新的策略.
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