本文選題：擁塞控制算法　切入點(diǎn)：分?jǐn)?shù)階擁塞控制模型　出處：《南京郵電大學(xué)》2017年碩士論文

【摘要】：互聯(lián)網(wǎng)在近十幾年的時(shí)間中獲得了高速發(fā)展,隨著用戶量的增多和通訊數(shù)據(jù)量的暴漲,網(wǎng)絡(luò)擁塞的問題越發(fā)突出。所以,設(shè)計(jì)并優(yōu)化擁塞控制算法、研究擁塞控制系統(tǒng)的動(dòng)力學(xué)行為,都成為了當(dāng)務(wù)之急。近幾年,分?jǐn)?shù)階微積分因其廣泛應(yīng)用成為了研究熱點(diǎn)。由于分?jǐn)?shù)階微分方程組能精確地刻畫現(xiàn)實(shí)世界中的很多現(xiàn)象,因此,研究這些分?jǐn)?shù)階數(shù)學(xué)模型的動(dòng)力學(xué)行為,包括穩(wěn)定性、分岔、混沌等,對(duì)于理解其代表的現(xiàn)象本身具有重要意義�；诜�(wěn)定性理論、分岔理論、分岔控制方法,本文主要考慮分?jǐn)?shù)階擁塞控制系統(tǒng)中的時(shí)滯對(duì)偶擁塞模型和指數(shù)RED模型,研究它們的穩(wěn)定性、Hopf分岔以及分岔控制問題。主要內(nèi)容如下:1)針對(duì)整數(shù)階對(duì)偶擁塞模型,設(shè)計(jì)帶有時(shí)滯反饋的混合控制器,研究受控系統(tǒng)的穩(wěn)定性與Hopf分岔問題。從增益系數(shù)的角度出發(fā),分析系統(tǒng)的特征方程,求出分岔閾值并證明Hopf分岔的發(fā)生�；旌峡刂茀�(shù)的引入和調(diào)節(jié),可以擴(kuò)大系統(tǒng)的穩(wěn)定域、延遲分岔。通過仿真,驗(yàn)證理論推導(dǎo)結(jié)果與混合控制的有效性。2)將分?jǐn)?shù)階微分引入指數(shù)RED模型,研究該分?jǐn)?shù)階系統(tǒng)的穩(wěn)定性和Hopf分岔特性。利用分?jǐn)?shù)階時(shí)滯微分方程組的穩(wěn)定性理論和分?jǐn)?shù)階時(shí)滯系統(tǒng)的Hopf分岔?xiàng)l件,選取增益系數(shù)作為分岔參數(shù),通過分析分?jǐn)?shù)階系統(tǒng)的特征方程,證明系統(tǒng)的局部穩(wěn)定性,求出分岔閾值并證明Hopf分岔的發(fā)生。當(dāng)增益系數(shù)達(dá)到分岔閾值時(shí),系統(tǒng)會(huì)發(fā)生Hopf分岔并在平衡點(diǎn)處產(chǎn)生周期振蕩。實(shí)驗(yàn)仿真證實(shí)了以上結(jié)果。3)在分?jǐn)?shù)階對(duì)偶擁塞模型的基礎(chǔ)上,設(shè)計(jì)分?jǐn)?shù)階PD控制器,分析受控分?jǐn)?shù)階系統(tǒng)的穩(wěn)定性和Hopf分岔特性。從時(shí)滯角度分析分?jǐn)?shù)階受控系統(tǒng)的特征方程,求出分岔閾值,分別給出漸近穩(wěn)定性和發(fā)生Hopf分岔的條件。調(diào)節(jié)控制器參數(shù),能使系統(tǒng)分岔提前或滯后發(fā)生。仿真結(jié)果證明了理論分析的結(jié)果,以及分?jǐn)?shù)階PD控制器對(duì)于改變系統(tǒng)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.

【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP393.06

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本文編號(hào)：1680397