Hopf bifurcation control in a congestion control model via dynamic delayed feedback

2008 ◽  
Vol 18 (4) ◽  
pp. 043104 ◽  
Author(s):  
Songtao Guo ◽  
Gang Feng ◽  
Xiaofeng Liao ◽  
Qun Liu
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Control Model ◽  
Delayed Feedback ◽  
Bifurcation Control

Hopf bifurcation control of congestion control model in a wireless access network

2014 ◽  
Vol 144 ◽  
pp. 159-168 ◽  
Author(s):  
Dawei Ding ◽  
Xuemei Qin ◽  
Tingting Wu ◽  
Nian Wang ◽  
Dong Liang
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Access Network ◽  
Control Model ◽  
Bifurcation Control ◽  
Wireless Access ◽  
Wireless Access Network

BIFURCATION CONTROL OF A CONGESTION CONTROL MODEL VIA STATE FEEDBACK

2013 ◽  
Vol 23 (06) ◽  
pp. 1330018 ◽  
Author(s):  
MIN XIAO ◽  
WEI XING ZHENG ◽  
JINDE CAO
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
State Feedback ◽  
Stability Domain ◽  
Control Model ◽  
The State ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Gain Parameter ◽  
State Feedback Controller

This paper proposes to use a state feedback method to control the Hopf bifurcation for a novel congestion control model, i.e. the exponential random early detection (RED) algorithm with a single link and a single source. The gain parameter of the congestion control model is chosen as the bifurcation parameter. The analysis shows that in the absence of the state feedback controller, the model loses stability via the Hopf bifurcation early, and can maintain a stationary sending rate only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses a stable sending rate in a larger parameter range. Furthermore, explicit formulae to determine the properties of the Hopf bifurcation are obtained. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control.

scholarly journals Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dawei Ding ◽  
Chun Wang ◽  
Lianghui Ding ◽  
Nian Wang ◽  
Dong Liang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Feedback Control ◽  
Congestion Control ◽  
State Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Fast Tcp ◽  
Hybrid Controller ◽  
Control Schemes

We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.

Hopf bifurcation in an Internet congestion control model

2004 ◽  
Vol 19 (4) ◽  
pp. 853-862 ◽  
Author(s):  
Chunguang Li ◽  
Guanrong Chen ◽  
Xiaofeng Liao ◽  
Juebang Yu
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Control Model ◽  
Internet Congestion Control ◽  
Internet Congestion

CONTROLLING HOPF BIFURCATION IN FLUID FLOW MODEL OF INTERNET CONGESTION CONTROL SYSTEM

2009 ◽  
Vol 19 (04) ◽  
pp. 1415-1424 ◽  
Author(s):  
DAWEI DING ◽  
JIE ZHU ◽  
XIAOSHU LUO ◽  
YULIANG LIU
Keyword(s):  
Fluid Flow ◽  
Control System ◽  
Hopf Bifurcation ◽  
Congestion Control ◽  
Flow Model ◽  
Delayed Feedback ◽  
Control Approach ◽  
Internet Congestion Control ◽  
Delayed Feedback Controller ◽  
Internet Congestion

In this paper, a time-delayed feedback controller is applied to a fluid flow model of Internet congestion control system in order to control Hopf bifurcation. It has been shown that the system without control loses stability and a Hopf bifurcation occurs when the bifurcation parameter, which is the communication delay of the model, passes through a critical value. Therefore, a control approach based on delayed feedback is proposed to postpone the onset of undesired Hopf bifurcation. Theoretical analysis and numerical simulations confirm that the controller is efficient in bifurcation control of the Internet congestion control system.

scholarly journals On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji chaotic system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jianping Shi ◽  
Liyuan Ruan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic System ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Delay Systems ◽  
Feedback Gain ◽  
Stability Of Equilibrium ◽  
Delayed Feedback Controller

Abstract In this paper, we study the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji (BG) chaotic system. Since the current study on Hopf bifurcation for fractional-order delay systems is carried out on the basis of analyses for stability of equilibrium of its linearized approximation system, it is necessary to verify the reasonability of linearized approximation. Through Laplace transformation, we first illustrate the equivalence of stability of equilibrium for a fractional-order delay Bhalekar–Gejji chaotic system and its linearized approximation system under an appropriate prior assumption. This semianalytically verifies the reasonability of linearized approximation from the viewpoint of stability. Then we theoretically explore the relationship between the time delay and Hopf bifurcation of such a system. By introducing the delayed feedback controller into the proposed system, the influence of the feedback gain changes on Hopf bifurcation is also investigated. The obtained results indicate that the stability domain can be effectively controlled by the proposed delayed feedback controller. Moreover, numerical simulations are made to verify the validity of the theoretical results.

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