状态依赖时滞耦合拥塞控制系统的振荡与同步

项目名称： 状态依赖时滞耦合拥塞控制系统的振荡与同步

项目编号： No.11502168

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 张舒

作者单位： 同济大学

项目金额： 22万元

中文摘要： 本项目为应用基础性研究，针对含有状态依赖时滞的计算机网络拥塞控制系统，通过（1）计算机网络中以状态依赖时滞为中心的复杂非线性动力学机制；（2）状态依赖时滞耦合网络的同步与去同步；（3）通过状态依赖时滞耦合的机械网络与计算机网络的稳定性与同步优化这三个科学问题的研究，深入认识计算机网络复杂动力学产生的机制，重点探索网络拓扑结构参数化的方法并完善状态依赖时滞系统的数值分岔算法；建立通过状态依赖时滞耦合的无线计算机网络和机器人网络的动力学方程，初步形成对耦合了计算机网络的机械网络进行分析和优化的方法。在本项目中，动力学的研究是基础，对状态依赖时滞的处理是关键，深刻认识状态依赖时滞耦合的计算机网络系统的复杂动力学及其机理、建立时滞同网络拓扑结构与网络同步模式之间的关系是本文研究的主要目标，这些研究将有助于对通过计算机网络进行通信和控制的机械网络设计恰当的控制并获得所需要的协同运动行为。

中文关键词： 时滞系统；非线性动力学；网络同步；拥塞控制；数值分岔分析

英文摘要： This project, which studies the system of Internet congestion control with state-dependent time delay, is a fundamental research in both theory and application. Based on the investigation on the following three scientific problems: (1) the mechanism of complicated dynamics induced by state-dependent delay in Internet; (2) synchronization and de-synchronization of state-dependent delay-coupled network; and (3) stability, synchronization and optimization of mechanical networks coupled with computer networks, we propose to further understand the origin of complicated dynamics of Internet and study the approach of parameterizing the network topology as well as developing the efficient algorithm of numerical bifurcation analysis for system with state-dependent delay. Also we plan to establish the equation of dynamics for state-dependent delay-coupled robot and wireless computer networks and then develop the method for analyzing and optimizing the coupled mechanical and computer networks. In this project, the research on the dynamical behavior of various network systems plays the fundamental role and the key problem is the treatment of state-dependent time delay. The main target of this project is to fully understand the mechanism of complicated dynamics of state-dependent delay-coupled computer networks and to uncover the relation among the delay, the network topology and various patterns of network synchronization. These results will help us to design the appropriate control scheme and obtain the desired collective motion of mechanical networks whose communication and control are realized through computer networks.

英文关键词： Time Delayed System;Nonlinear Dynamics;Network Synchronizaton;Congestion Control;Numerical Bifurcation Analysis