scholarly journals Dynamics of a Duopoly Game with Two Different Delay Structures

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Shumin Jiang ◽  
Fei Xu ◽  
Zhanwen Ding ◽  
Chen Yang ◽  
Huanhuan Liu
Keyword(s):  
Time Delay ◽  
Market Price ◽  
Period Doubling ◽  
System Stability ◽  
Delayed Feedback Control ◽  
System Control ◽  
Heterogeneous Players ◽  
Cournot Game ◽  
The Stability ◽  
Time Delayed Feedback

Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

scholarly journals Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3223 ◽  
Author(s):  
Liu ◽  
Zhang ◽  
Zou
Keyword(s):  
Time Delay ◽  
Power System ◽  
Closed Loop ◽  
Frequency Control ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Linear Matrix ◽  
Closed Loop System ◽  
The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

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.

scholarly journals Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Changjin Xu ◽  
Peiluan Li ◽  
Maoxin Liao ◽  
Zixin Liu ◽  
Qimei Xiao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Feedback Controllers ◽  
Control Scheme ◽  
The Stability ◽  
Time Delayed Feedback

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

Simulation and Control of a Duopoly Model

2014 ◽  
Vol 472 ◽  
pp. 146-151
Author(s):  
Ya Li Lu
Keyword(s):  
Nash Equilibrium ◽  
Demand Function ◽  
Delayed Feedback Control ◽  
Control Scheme ◽  
Duopoly Model ◽  
Adjustment Speed ◽  
The Stability ◽  
Boundary Fixed Points ◽  
And Control ◽  
Time Delayed Feedback

This paper studies the dynamics of a duopoly model with bounded rationality and nonlinear demand function. Based on the stability theorem and Jurys criterions, we prove that the model has two unstable boundary fixed points and a local stable Nash equilibrium. Then we depict the stability region of Nash equilibrium, and investigate the effects of output adjustment speed on the players profit respectively. Theoretical analysis and simulations show that higher output adjustment speed can result in chaotic variation of outputs, and that the Nash equilibrium is the optimal result of duopoly game. To improve the profitability of each player and achieve the optimal game result, we put forth a new scheme combined with the time-delayed feedback control and the limiter control to stabilize the output to Nash equilibrium. Finally, the numerical simulation is adopted to verify the effectiveness and feasibility of the above control scheme.

Active Vibration Suppression With Time Delayed Feedback

2003 ◽  
Vol 125 (3) ◽  
pp. 384-388 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
System Stability ◽  
Delayed Systems ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

Gobal Optimization Based Power System Stablization with WAMS Time Delay Study

2012 ◽  
Vol 433-440 ◽  
pp. 7362-7367
Author(s):  
Zhang Lin ◽  
Di Chen Liu ◽  
Wu Jun ◽  
Qing Fen Liao ◽  
Yun Lei ◽  
...  
Keyword(s):  
Global Optimization ◽  
Time Delay ◽  
Power System ◽  
Low Frequency ◽  
System Stability ◽  
Area Measurement ◽  
Wide Area ◽  
Linear Matrix ◽  
Feedback Signal ◽  
The Stability

It is very important to take into consideration time delay in wide area power system stability; the design of PSS (Power System Stabilizer) should consider global optimization with WAMS (Wide Area Measurement System) time delay. Newly designed PSS should be insensitive to time delay and suppress internal low frequency oscillations. It is used as feedback signal and is real-time synchronous that WAMS signal shows. Power system is modeled with the consideration of time delay. LMI (Linear Matrix Inequalities) is used to solve the stability condition of time delay system. Based on the time-delay effect of the wide-area measurement signals, this paper redesigned the PSS with global optimization of power system. The attached two-area-four-machine system simulation illustrates that wide-area PSS designed by global optimization with the consideration of time-delay can limit internal low frequency oscillation with time-delay insensitivity, and improve the stability of power system. It implements global optimization of PSS with WAMS time delay stability.

Nonlinear Dynamic Analysis of a Simplest Fractional-Order Delayed Memristive Chaotic System

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Wei Hu ◽  
Dawei Ding ◽  
Nian Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Transversality Condition ◽  
Memristive System ◽  
Route To Chaos ◽  
The Stability

A simplest fractional-order delayed memristive chaotic system is investigated in order to analyze the nonlinear dynamics of the system. The stability and bifurcation behaviors of this system are initially investigated, where time delay is selected as the bifurcation parameter. Some explicit conditions for describing the stability interval and the transversality condition of the emergence for Hopf bifurcation are derived. The period doubling route to chaos behaviors of such a system is discussed by using a bifurcation diagram, a phase diagram, a time-domain diagram, and the largest Lyapunov exponents (LLEs) diagram. Specifically, we study the influence of time delay on the chaotic behavior, and find that when time delay increases, the transitions from one cycle to two cycles, two cycles to four cycles, and four cycles to chaos are observed in this system model. Corresponding critical values of time delay are determined, showing the lowest orders for chaos in the fractional-order delayed memristive system. Finally, numerical simulations are provided to verify the correctness of theoretical analysis using the modified Adams–Bashforth–Moulton method.

Chaos Suppression via Integrative Time Delay Control

2020 ◽  
Vol 30 (14) ◽  
pp. 2050208
Author(s):  
Ayman A. Arafa ◽  
Yong Xu ◽  
Gamal M. Mahmoud
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Time Interval ◽  
General Strategy ◽  
Normal Form Theory ◽  
Chaos Suppression ◽  
Form Theory ◽  
The Stability ◽  
Time Delayed Feedback

A general strategy for suppressing chaos in chaotic Burke–Shaw system using integrative time delay (ITD) control is proposed, as an example. The idea of ITD is that the feedback is integrated over a time interval. Physically, the chaotic system responds to the average information it receives from the feedback. The main feature of integrative is that the stability of the chaotic system occurs over a wider range of the space parameters. Controlling chaotic systems with ITD has not been discussed before as far as we know. Stability and the existence of Hopf bifurcation are studied which demonstrate that the switch stability occurs at critical values of the time delay. Employing the normal form theory and center manifold argument, an explicit formula is derived to determine the stability and the direction of the bifurcating periodic solutions. Numerically, the bifurcation diagram and the eigenvalues of the corresponding characteristic equations are computed to supply a clear interpretation for suppressing chaos via ITD. Furthermore, ITD method is compared with the time delayed feedback (TDF) control numerically. This comparison shows that the stability area with ITD is larger than TDF which demonstrates the feasibility and effectiveness of the ITD. Other examples of chaotic systems can be similarly investigated.

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