Hopf bifurcation control via a dynamic state-feedback control

2012 ◽  
Vol 376 (4) ◽  
pp. 442-446 ◽  
Author(s):  
Le Hoa Nguyen ◽  
Keum-Shik Hong
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Bifurcation Control ◽  
Dynamic State

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.

scholarly journals State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

2021 ◽  
Vol 11 (22) ◽  
pp. 10568
Author(s):  
Kamil Borawski
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Discrete Time ◽  
State Feedback ◽  
Matrix Pencil ◽  
State Feedback Control ◽  
Drazin Inverse ◽  
Dynamic State ◽  
Static State ◽  
Order Linear

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used to show the efficacy of the presented approach. Our considerations were based on the Drazin inverse matrix method.

Control of the Hopf Bifurcation by a Linear Feedback Control

2015 ◽  
Vol 25 (01) ◽  
pp. 1550006 ◽  
Author(s):  
J. A. López-Renteria ◽  
F. Verduzco ◽  
B. Aguirre-Hernández
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Linear State

In this work, we design a kind of linear state feedback control, via the roots connecting-curve, for a class of nonlinear systems which permits to control the Hopf bifurcation. An illustrative example is given.

scholarly journals Double Hopf Bifurcation of a Hematopoietic System with State Feedback Control

2018 ◽  
Vol 10 (4) ◽  
pp. 116
Author(s):  
Suqi Ma
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
State Feedback ◽  
Threshold Value ◽  
State Feedback Control ◽  
Hematopoietic Stem ◽  
Double Hopf Bifurcation ◽  
Periodical Solution ◽  
Varying Time Delay ◽  
Manifold Theory

The dynamics of a system composed of hematopoietic stem cells and its relationship with neutrophils is ubiquitous due to periodic oscillating behavior induce cyclical neutropenia. Underlying the methodology of state feedback control with two time delays, double Hopf bifurcation occurs as varying time delay to reach its threshold value. By applying center manifold theory, the analytical analysis of system exposed the different dynamical feature in the classified regimes near double Hopf point. The novel dynamics as periodical solution and quasi-periodical attractor coexistence phenomena are explored and verified  by numerical simulation.

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