scholarly journals Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhe Zhang ◽  
Jing Zhang ◽  
Fan Yong Cheng ◽  
Feng Liu ◽  
Can Ding
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Impulse Control ◽  
Impulsive Control ◽  
Financial System ◽  
Stability Control ◽  
Two Dimensions ◽  
State Variable ◽  
The Stability ◽  
System With Time Delay

AbstractThis paper is concerned about the impulsive control of a class of novel nonlinear fractional-order financial system with time-delay. Considering the variation of every states in the fractional-order financial system in the real world has certain delay for various reasons, thus we add corresponding delay on every state variable. Different from the traditional method of stability judgment, we choose two dimensions of time and space to analyze, which makes the process more accurate. In addition, the sufficient condition of the stability criterion for the fractional-order financial system based on impulsive control is derived. Moreover, the impulsive control can not only make the fractional-order financial system stable in different time delay but also in the different fractional operator. Consequently, the impulsive control has generality, universality and strong applicability. In the end, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed method.

scholarly journals Stability and Hopf bifurcation analysis of fractional order nonlinear financial system with time delay

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Laplace Transformation ◽  
Financial System ◽  
System With Time Delay

In this paper, we study a fractional order time delay for nonlinear financial system. By using Laplace transformation, stability and Hopf bifurcation analysis have been done for the model. Furthermore, numerical simulation has been carried out for better understanding of our results.

scholarly journals A New Design Method for PI-PD Control of Unstable Fractional-Order System with Time Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Min Zheng ◽  
Tao Huang ◽  
Guangfeng Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Graphical Method ◽  
Stability Boundary ◽  
Fractional Order System ◽  
Stable Region ◽  
Order System ◽  
Pd Controller ◽  
The Stability ◽  
System With Time Delay

In this paper, a practical PI-PD controller parameter tuning method is proposed, which uses the incenter of the triangle and the Fermat point of the convex polygon to optimize the PI-PD controller. Combined with the stability boundary locus method, the PI-PD controller parameters that can ensure stability for the unstable fractional-order system with time delay are obtained. Firstly, the parameters of the inner-loop PD controller are determined by the centre coordinates of the CSR in the kd−kf plane. Secondly, a new graphical method is used to calculate the parameters of the PI controller, in which Fermat points in the CSR of (kp−ki) plane are selected. Furthermore, the method is extended to uncertain systems, and the PI-PD controller parameters are obtained by using the proposed method through common stable region of all stable regions. The proposed graphical method not only ensures the stability of the closed-loop system but also avoids the complicated optimization calculations. The superior control performance of this method is illustrated by simulation.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

scholarly journals Development of Temperature Process Control Method Using Smith Predictor

2019 ◽  
Vol 111 ◽  
pp. 06016
Author(s):  
Nikolajs Bogdanovs ◽  
Romualds Beļinskis ◽  
Ernests Petersons ◽  
Andris Krūmiņš ◽  
Artūrs Brahmanis
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Distributed Delay ◽  
Heating System ◽  
Smith Predictor ◽  
Hot Water ◽  
Test Bed ◽  
Hot Water Supply ◽  
The Stability ◽  
System With Time Delay

The analysis of a problem of development of control systems for objects with big time delay is carried out in this work. For such objects it is difficult to provide high-quality control, because the control is carried on the last status of object’s output. The main setup methods of PID regulators have been examined. Based on this analysis the technique of complete synthesis of the regulator of higher level is given in order to regulate building’s heating system. This work offers a new method of object’s control with distributed delay. As the test bed for the offered structure of control the valve of hot water supply in a heat-node is used. Using the test bed the stability of the system with time delay have been studied, which is controlled by the PID-regulator assisted by Smith Predictor used to compensate the dead time.

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