scholarly journals Double Delayed Feedback Control of a Nonlinear Finance System

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhichao Jiang ◽  
Yanfen Guo ◽  
Tongqian Zhang
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Chaotic Behavior ◽  
Threshold Value ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Finance System ◽  
Stable Periodic ◽  
The Stability ◽  
Manifold Theory

In this paper, a class of chaotic finance system with double delayed feedback control is investigated. Firstly, the stability of equilibrium and the existence of periodic solutions are discussed when delays change and cross some threshold value. Then the properties of the branching periodic solutions are given by using center manifold theory. Further, we give an example and numerical simulation, which implies that chaotic behavior can be transformed into a stable equilibrium or a stable periodic solution. Also, we give the local sensitivity analysis of parameters on equilibrium.

Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Mehdi Tabe Arjmand ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Single Mode ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Model Parameters ◽  
Unstable Periodic Orbits ◽  
Single Mode Approximation

The taping mode Atomic Force Microscopic (T-AFM) can be properly described by a sinusoidal excitation of its base and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In this paper a nonlinear delayed feedback control is proposed to control chaos in a single mode approximation of a T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The effectiveness of the presented methods is numerically verified and the results show the high performance of the controller.

An Efficient Approach for Stability Analysis and Parameter Tuning in Delayed Feedback Control of a Flying Robot Carrying a Suspended Load

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Wei Dong ◽  
Ye Ding ◽  
Luo Yang ◽  
Xinjun Sheng ◽  
Xiangyang Zhu
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Spectral Radius ◽  
Stability Region ◽  
Parameter Tuning ◽  
Suspended Load ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
The Stability ◽  
Flying Robot

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

Delayed Feedback Control and Bifurcation Analysis in a Chaotic Chemostat System

2015 ◽  
Vol 25 (06) ◽  
pp. 1550087 ◽  
Author(s):  
Zhichao Jiang ◽  
Wanbiao Ma
Keyword(s):  
Center Manifold ◽  
Chaotic Oscillation ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Stable Steady State ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Stable Periodic ◽  
Form Theory ◽  
The Stability

In this paper, the effect of delay on a nonlinear chaotic chemostat system with delayed feedback is investigated by regarding delay as a parameter. At first, the stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, some numerical simulation examples are given, which indicate that the chaotic oscillation can be converted into a stable steady state or a stable periodic orbit when delay passes through certain critical values.

STABILIZATION OF UNSTABLE PERIODIC SOLUTIONS BY NONLINEAR RECURSIVE DELAYED FEEDBACK CONTROL

2006 ◽  
Vol 16 (10) ◽  
pp. 2935-2947 ◽  
Author(s):  
JIANDONG ZHU ◽  
YU-PING TIAN
Keyword(s):  
Periodic Solutions ◽  
Closed Loop ◽  
Control Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Closed Loop System ◽  
Delayed Feedback Controller ◽  
The Stability ◽  
Geometry Method ◽  
Odd Number Limitation

This paper considers stabilization of unstable periodic solutions of nonlinear systems. Based on differential geometry method, a nonlinear recursive delayed feedback controller is designed. The concept of γ dynamics is introduced and the stability of the periodic solution of the closed-loop system is proved rigorously. The proposed control method does not have the odd number limitation. Simulation results are also presented for validating the effectiveness of the proposed method.

scholarly journals Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Rongyan Zhang
Keyword(s):  
Center Manifold ◽  
Chaotic Oscillation ◽  
Delayed Feedback ◽  
Stable Steady State ◽  
Normal Form Theory ◽  
Finance System ◽  
Stable Periodic ◽  
Form Theory ◽  
The Stability ◽  
Time Delayed Feedback

A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction, and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit.

Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Kaveh Merat ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Electrical Circuit ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Parameter Uncertainties ◽  
First Order

In this paper a nonlinear delayed feedback control is proposed to control chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs). Firstly, the system parameters assumed to be known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then the sliding mode scheme of the proposed controller is presented in presence of model parameter uncertainties. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first order periodic orbit and is compared with a typical linear delayed feedback control. Simulation results show the high performance of the methods for chaos elimination in Sprott circuit.

STABILITY AND BIFURCATION ANALYSIS IN A DIFFUSIVE BRUSSELATOR SYSTEM WITH DELAYED FEEDBACK CONTROL

2012 ◽  
Vol 22 (02) ◽  
pp. 1250037 ◽  
Author(s):  
WENJIE ZUO ◽  
JUNJIE WEI
Keyword(s):  
Feedback Control ◽  
Functional Differential Equations ◽  
Turing Instability ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Brusselator Model ◽  
Constant Equilibrium ◽  
The Stability

A diffusive Brusselator model with delayed feedback control subject to Dirichlet boundary condition is considered. The stability of the unique constant equilibrium and the existence of a family of inhomogeneous periodic solutions are investigated in detail, exhibiting rich spatiotemporal patterns. Moreover, it shows that Turing instability occurs without delay. And under certain conditions, the constant equilibrium switches finite times from stability to instability to stability, and becomes unstable eventually, as the delay crosses through some critical values. Then, the direction and the stability of Hopf bifurcations are determined by the normal form theory and the center manifold reduction for partial functional differential equations. Finally, some numerical simulations are carried out for illustrating the analysis results.

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