A Common Control Method of Three-Dimension Chaotic System

2012 ◽  
Vol 1 (2) ◽  
pp. 131-136
Author(s):  
Jun Kang ◽  
Wenjun Meng
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Three Dimension ◽  
Common Control

scholarly journals A Novel Three Dimension Autonomous Chaotic System with a Quadratic Exponential Nonlinear Term

2012 ◽  
Vol 2 (2) ◽  
pp. 209-215 ◽  
Author(s):  
F. Yu ◽  
C. Wang
Keyword(s):  
Chaotic System ◽  
Nonlinear Term ◽  
Cross Product ◽  
Three Dimension ◽  
Compound Structure ◽  
Compensation Circuit ◽  
Forming Mechanism ◽  
Product Term ◽  
Practical Engineering ◽  
Cross Product Term

A novel three dimension autonomous (3D) chaotic system with a quadratic exponential nonlinear term and a quadratic cross-product term is described in this paper. The basic dynamical properties of the new attractor are studied. The forming mechanism of its compound structure, obtained by merging together two simple attractors after performing one mirror operation, has been investigated by detailed numerical as well as theoretical analysis. Finally, the exponential operation circuit and its temperature-compensation circuit, which makes the new system more applicable from a practical engineering perspective, are investigated.

Position Domain PD Control for Contour Tracking

2010 ◽  
Author(s):  
P. R. Ouyang ◽  
Truong Dam
Keyword(s):  
Motion Tracking ◽  
Control Method ◽  
Tracking Error ◽  
Original System ◽  
Contour Tracking ◽  
Pd Control ◽  
Tracking Errors ◽  
Motion System ◽  
Common Control ◽  
The Time Domain

For multi-axis motion control applications, contour tracking is one of the most common control problems encountered by industrial manipulators and robots. In this paper, a position domain PD control method is proposed for the purpose of improving the contour tracking performance. To develop the new control method, the multi-axis motion system is viewed as a master-slave motion system where the master motion is sampled equidistantly and used as an independent variable, while the slave motions are described as functions of the master motion according to the contour tracking requirements. The dynamic model of the multi-axis motion system is developed in the position domain based on the master motion by transforming the original system dynamic equations from the time domain to the position domain. In this control methodology, the master motion will yield zero tracking error for the position as it is used as reference, and only the slave motion tracking errors will affect the final contour tracking errors. The proposed position domain PD controller is successfully examined in a Cartesian robotic system for linear motion tracking and circular contour tracking.

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

scholarly journals A Financial Chaotic System Control Method Based on Intermittent Controller

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xia Lu
Keyword(s):  
Financial Crisis ◽  
Chaotic System ◽  
Control Method ◽  
Negative Impact ◽  
Financial System ◽  
Practical Significance ◽  
System Control ◽  
Social Stability ◽  
Intermittent Feedback ◽  
Range Of Values

Finance is the core of modern economy. The security and stability of the financial system is the key to stable economic and social development. During the operation of the financial system, financial chaos such as the severe turbulence of the financial market and the financial crisis occurred due to deterministic instability, which brought a great negative impact on economic growth and social stability. For the financial chaotic system, an intermittent feedback controller is designed in this paper. By adjusting the controller parameters, the financial system can be controlled from chaotic to periodic evolution. First, the dynamic equations and controllers of the financial system are analyzed and the range of values of the controller parameters is theoretically obtained. Then, the influence of parameters on the system is studied, and the feasibility of the proposed method is proved by numerical simulation. Finally, the practical significance of the controller on the macrocontrol of the financial crisis is discussed. It is theoretically proven that when the financial crisis comes, the financial system can be stabilized more quickly through appropriate control methods.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

ON IMPULSIVE CONTROL AND ITS APPLICATION TO CHEN'S CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1191-1197 ◽  
Author(s):  
ZHI-HONG GUAN ◽  
RUI-QUAN LIAO ◽  
FENG ZHOU ◽  
HUA O. WANG
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Asymptotical Stability ◽  
Impulsive Systems ◽  
Chaotic State ◽  
Chaos Suppression ◽  
Zero Equilibrium

In this paper, impulsive control of nonlinear systems and its application to Chen's chaotic system are considered. A new impulsive control method for chaos suppression, using Chen's system as an example, is developed. Some new general criteria for exponential stability and asymptotical stability of nonlinear impulsive systems are established and, particularly, some simple conditions sufficient for driving the chaotic state of Chen's system to its zero equilibrium are presented.

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