# American Institute of Mathematical Sciences

September  2011, 16(2): 653-668. doi: 10.3934/dcdsb.2011.16.653

## Time-varying delayed feedback control for an internet congestion control model

 1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China, China

Received  February 2010 Revised  November 2010 Published  June 2011

A proportionally-fair controller with time delay is considered to control Internet congestion. The time delay is chosen to be a controllable parameter. To represent the relation between the delay and congestion analytically, the method of multiple scales is employed to obtain the periodic solution arising from the Hopf bifurcation in the congestion control model. A new control method is proposed by perturbing the delay periodically. The strength of the perturbation is predicted analytically in order that the oscillation may disappear gradually. It implies that the proved control scheme may decrease the possibility of the congestion derived from the oscillation. The proposed control scheme is verified by the numerical simulation.
Citation: Shu Zhang, Jian Xu. Time-varying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 653-668. doi: 10.3934/dcdsb.2011.16.653
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##### References:
 [1] Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221 [2] Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021010 [3] Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, , () : -. doi: 10.3934/era.2021022 [4] Bingru Zhang, Chuanye Gu, Jueyou Li. Distributed convex optimization with coupling constraints over time-varying directed graphs†. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2119-2138. doi: 10.3934/jimo.2020061 [5] Qigang Yuan, Jingli Ren. Periodic forcing on degenerate Hopf bifurcation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2857-2877. doi: 10.3934/dcdsb.2020208 [6] Changjun Yu, Lei Yuan, Shuxuan Su. A new gradient computational formula for optimal control problems with time-delay. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021076 [7] Wensheng Yin, Jinde Cao, Guoqiang Zheng. Further results on stabilization of stochastic differential equations with delayed feedback control under $G$-expectation framework. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021072 [8] Seddigheh Banihashemi, Hossein Jafaria, Afshin Babaei. A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021025 [9] Tobias Breiten, Sergey Dolgov, Martin Stoll. Solving differential Riccati equations: A nonlinear space-time method using tensor trains. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 407-429. doi: 10.3934/naco.2020034 [10] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 [11] Haili Qiao, Aijie Cheng. A fast high order method for time fractional diffusion equation with non-smooth data. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021073 [12] Fabio Camilli, Serikbolsyn Duisembay, Qing Tang. Approximation of an optimal control problem for the time-fractional Fokker-Planck equation. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021013 [13] Claudianor O. Alves, Giovany M. Figueiredo, Riccardo Molle. Multiple positive bound state solutions for a critical Choquard equation. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021061 [14] Jing Feng, Bin-Guo Wang. An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3069-3096. doi: 10.3934/dcdsb.2020220 [15] Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021020 [16] Wenjing Liu, Rong Yang, Xin-Guang Yang. Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021052 [17] V. Vijayakumar, R. Udhayakumar, K. Kavitha. On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay. Evolution Equations & Control Theory, 2021, 10 (2) : 271-296. doi: 10.3934/eect.2020066 [18] Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 [19] Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 [20] Woocheol Choi, Youngwoo Koh. On the splitting method for the nonlinear Schrödinger equation with initial data in $H^1$. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3837-3867. doi: 10.3934/dcds.2021019

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