Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple 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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BIFURCATION CONTROL OF A CONGESTION CONTROL MODEL VIA STATE FEEDBACK

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413300188 ◽

2013 ◽

Vol 23 (06) ◽

pp. 1330018 ◽

Cited By ~ 19

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.

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Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418500426 ◽

2018 ◽

Vol 28 (03) ◽

pp. 1850042 ◽

Cited By ~ 16

Author(s):

Xin-You Meng ◽

Yu-Qian Wu

Keyword(s):

Hopf Bifurcation ◽

Time Delay ◽

State Feedback ◽

Critical Value ◽

Feedback Controller ◽

Bifurcation Parameter ◽

State Feedback Controller ◽

Interior Equilibrium ◽

Fish Model ◽

Singularity Induced Bifurcation

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

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Design of Observer-Based Feedback Control for Time-Delay Systems With Application to Automotive Powertrain Control

ASME 2009 Dynamic Systems and Control Conference, Volume 2 ◽

10.1115/dscc2009-2590 ◽

2009 ◽

Cited By ~ 1

Author(s):

Sun Yi ◽

Patrick W. Nelson ◽

A. Galip Ulsoy

Keyword(s):

Time Delay ◽

Feedback Control ◽

State Feedback ◽

Feedback Controller ◽

State Feedback Control ◽

Delay Systems ◽

Lambert W Function ◽

Actual State ◽

Time Delay Systems ◽

New Approach

A new approach for observer-based feedback control of time-delay systems is developed. Time-delays in systems lead to characteristic equations of infinite dimension, making the systems difficult to handle with classical control methods. In this paper, a recently developed approach, based on the Lambert W function, is used to address this difficulty and to control time-delay systems by designing an observer-based state feedback controller via eigenvalue assignment. The designed observer provides estimation of the state, which converges asymptotically to the actual state, and is then used for state feedback control. The feedback controller and the observer take simple linear forms and, thus, are easy to implement when compared to nonlinear methods. This new approach is applied, for illustration, to the control of a diesel engine to achieve improvement in fuel efficiency and reduction in emissions. The simulation results show excellent closed-loop performance.

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