分数阶拥塞控制系统的Hopf分岔与控制

发布时间：2018-03-29 08:46

本文选题：拥塞控制算法　切入点：分数阶拥塞控制模型　出处：《南京邮电大学》2017年硕士论文

【摘要】：互联网在近十几年的时间中获得了高速发展,随着用户量的增多和通讯数据量的暴涨,网络拥塞的问题越发突出。所以,设计并优化拥塞控制算法、研究拥塞控制系统的动力学行为,都成为了当务之急。近几年,分数阶微积分因其广泛应用成为了研究热点。由于分数阶微分方程组能精确地刻画现实世界中的很多现象,因此,研究这些分数阶数学模型的动力学行为,包括稳定性、分岔、混沌等,对于理解其代表的现象本身具有重要意义。基于稳定性理论、分岔理论、分岔控制方法,本文主要考虑分数阶拥塞控制系统中的时滞对偶拥塞模型和指数RED模型,研究它们的稳定性、Hopf分岔以及分岔控制问题。主要内容如下:1)针对整数阶对偶拥塞模型,设计带有时滞反馈的混合控制器,研究受控系统的稳定性与Hopf分岔问题。从增益系数的角度出发,分析系统的特征方程,求出分岔阈值并证明Hopf分岔的发生。混合控制参数的引入和调节,可以扩大系统的稳定域、延迟分岔。通过仿真,验证理论推导结果与混合控制的有效性。2)将分数阶微分引入指数RED模型,研究该分数阶系统的稳定性和Hopf分岔特性。利用分数阶时滞微分方程组的稳定性理论和分数阶时滞系统的Hopf分岔条件,选取增益系数作为分岔参数,通过分析分数阶系统的特征方程,证明系统的局部稳定性,求出分岔阈值并证明Hopf分岔的发生。当增益系数达到分岔阈值时,系统会发生Hopf分岔并在平衡点处产生周期振荡。实验仿真证实了以上结果。3)在分数阶对偶拥塞模型的基础上,设计分数阶PD控制器,分析受控分数阶系统的稳定性和Hopf分岔特性。从时滞角度分析分数阶受控系统的特征方程,求出分岔阈值,分别给出渐近稳定性和发生Hopf分岔的条件。调节控制器参数,能使系统分岔提前或滞后发生。仿真结果证明了理论分析的结果,以及分数阶PD控制器对于改变系统分岔的有效性。
[Abstract]:The Internet has gained rapid development in recent years, with the soaring increase of the amount of user data and communication, network congestion problems become more prominent. Therefore, the design and optimization of congestion control algorithm, dynamic behavior of the congestion control system, has become the most urgent task. In recent years, the fractional calculus because of its wide application has become a research hotspot. As the fractional differential equations can accurately describe many phenomena in the real world, therefore, dynamic behavior, study these fractional mathematical model including stability, bifurcation, chaos, has important significance for understanding on behalf of the phenomenon itself. Based on the stability theory, bifurcation theory bifurcation control method, this paper considers the fractional time delay dual congestion congestion control model and exponential model of RED system, study the stability, Hopf bifurcation and bifurcation control The problem. The main contents are as follows: 1) the integer order dual congestion model, hybrid controller design with delay feedback, stability and Hopf bifurcation problems of the controlled system. Starting from the angle of gain coefficient, the characteristic equation analysis system, calculate the bifurcation threshold and proved that Hopf bifurcation occurs. The mixed control parameters and the introduction of regulation that can enlarge the stability region of the system delay bifurcation. The simulation results verify the theoretical derivation and the effectiveness of the hybrid control.2) will introduce fractional differential index RED model to study the fractional order system stability and Hopf bifurcation. Hopf bifurcation conditions using fractional order delay differential equations and the stability theory of fractional order time delay the selection of the gain coefficient as the bifurcation parameter, the characteristic equation of fractional order system, local stability proof system, calculate the bifurcation threshold and prove Hopf The fork occurred. When the gain coefficient reaches the bifurcation threshold, the system will generate the Hopf bifurcation and periodic oscillation at the equilibrium point. The simulation experiments confirmed the results of the above.3) based on fractional dual congestion model, fractional order PD controller design, controlled analysis of fractional order system stability and Hopf bifurcation analysis features. Equation of fractional order control system from the angle of delay, calculate the bifurcation threshold are given asymptotic stability and Hopf bifurcation conditions. The controller can make the system bifurcation in advance or delay. The simulation results show that the results of the theoretical analysis, and the fractional order PD controller is effective in changing the system bifurcation.

【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP393.06

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