Hopf bifurcation control for a fluid flow model of internet congestion control systems via state feedback

2014 ◽  
Vol 33 (1) ◽  
pp. 69-93 ◽  
Author(s):  
Wenying Xu ◽  
Tasawar Hayat ◽  
Jinde Cao ◽  
Min Xiao
Keyword(s):  
Fluid Flow ◽  
Hopf Bifurcation ◽  
Congestion Control ◽  
Control Systems ◽  
State Feedback ◽  
Flow Model ◽  
Bifurcation Control ◽  
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.

Bifurcation Analysis of a Class of (n + 1)-Dimension Internet Congestion Control Systems

2015 ◽  
Vol 25 (02) ◽  
pp. 1550019 ◽  
Author(s):  
Wenying Xu ◽  
Jinde Cao ◽  
Min Xiao
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Control Systems ◽  
Large Scale ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Characteristic Roots ◽  
Internet Congestion Control ◽  
Internet Congestion ◽  
The Stability

This paper investigates the stability and Hopf bifurcation induced by the time delay in a class of (n + 1)-dimension Internet congestion control systems. Although there are several previous works on simplified models of Internet congestion systems with only one or two sources and such works can reflect partly dynamical behaviors of real Internet systems, some complicated problems may inevitably be overlooked. Hence, it is meaningful to study high-dimensional models which stand closer to general realistic large-scale Internet congestion networks. By analyzing the distribution of the associated characteristic roots, we can obtain conditions for keeping systems stable. When the delay increases and exceeds a critical value, the system will undergo a Hopf bifurcation. Furthermore, the explicit formulas to determine the stability and the direction of the bifurcating periodic solution are derived by applying the normal form theory and the center manifold reduction. Finally, two numerical examples are given to verify our theoretical analysis.

ANALYSIS OF HOPF BIFURCATION FOR AN INTERNET CONGESTION CONTROL SYSTEM

2007 ◽  
Vol 40 (12) ◽  
pp. 639-644 ◽  
Author(s):  
Mohammad Reza ◽  
Jahed Motlagh ◽  
Behrooz Rezaie ◽  
Siavash Khorsandi ◽  
Morteza Analoui
Keyword(s):  
Control System ◽  
Hopf Bifurcation ◽  
Congestion Control ◽  
Internet Congestion Control ◽  
Internet Congestion

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.

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