Synchronization, anti-synchronization and circuit realization of a novel hyper-chaotic system

Circuit World ◽  
2018 ◽  
Vol 44 (3) ◽  
pp. 132-149 ◽  
Author(s):  
Yanjun Lu ◽  
Li Xiong ◽  
Yongfang Zhang ◽  
Peijin Zhang ◽  
Cheng Liu ◽  
...  
Keyword(s):  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Chaotic Attractors ◽  
The Novel ◽  
Electronic Circuits ◽  
Content Type ◽  
Simulation Results ◽  
Physical Components

Purpose This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Design/methodology/approach The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors. Findings Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist. Originality/value The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

Stabilization and circuit implementation of a novel chemical oscillating chaotic system

Circuit World ◽  
2019 ◽  
Vol 45 (2) ◽  
pp. 93-106
Author(s):  
Li Xiong ◽  
Wanjun Yin ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
The Novel ◽  
Content Type ◽  
Initial Values ◽  
Parameters Selection ◽  
Chaotic Circuits ◽  
Simulation Results

Purpose This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated. Design/methodology/approach The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters. Findings It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits. Originality/value The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.

scholarly journals Coexisting attractors, chaos control and synchronization in a self-exciting homopolar dynamo system

2020 ◽  
Vol 13 (2) ◽  
pp. 167-179
Author(s):  
Xingrong Chen ◽  
Li Xiao ◽  
Sifeu Takougang Kingni ◽  
Irene Moroz ◽  
Zhouchao Wei ◽  
...  
Keyword(s):  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Control ◽  
Lyapunov Stability Theory ◽  
Control Signal ◽  
Coexisting Attractors ◽  
Content Type ◽  
Single Controller ◽  
Control And Synchronization

PurposeThe purpose of this paper is to investigate coexisting attractors, chaos control and synchronization in a self-exciting homopolar dynamo system in this paper.Design/methodology/approachTwo single controllers are designed and added to the proposed 3D autonomous chaotic system, and its stability at zero equilibrium point is guaranteed by applying an appropriate control signal based on the Lyapunov stability theory.FindingsNumerical simulations reveal that the proposed 3D dynamo system exhibits periodic oscillations, double-scroll chaotic attractors and coexisting attractors. Finally, a single controller is designed for the global asymptotic synchronization of a unidirectionally coupled identical 3D autonomous chaotic system.Originality/valueThe derived results of this paper are new and complement some earlier works. The innovation concludes two points in this paper; coexisting attractors are foundthe and an appropriate control signal based on the Lyapunov stability theory is established. The ideas of this paper can be applied to investigate some other homopolar dynamo systems.

Adaptive Attitude Control on Multiple Independently Targeted Reentry Vehicles (MIRV)

2014 ◽  
Vol 494-495 ◽  
pp. 1316-1319
Author(s):  
Xing Yu Chen ◽  
Fan Li ◽  
Jian Hui Zhao ◽  
Zhao Long Fan
Keyword(s):  
Numerical Simulation ◽  
Control System ◽  
Lyapunov Stability ◽  
Attitude Control ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Attitude Dynamics ◽  
Dynamics Model ◽  
Simulation Results

Based on the characteristics of releasing loads for many times, the attitude dynamics model of MIRV has established by using the Rodrigues representation, and we proposed a method of indirect multi-model adaptive attitude control. It was proved that the adaptive controller we designed can ensure the control system globally uniformly and bounded stable according to the Lyapunov stability theory, and the effectiveness of the controller was demonstrated by the numerical simulation results.

scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

scholarly journals Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chunhua Cheng ◽  
Fengjuan Gao ◽  
Jingshuo Xu ◽  
Yuanxin Wang ◽  
Tao Yuan
Keyword(s):  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Input Saturation ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure.

Synchronization of Incommensurate Fractional-Order Chaotic System Using Adaptive Control

2014 ◽  
Vol 602-605 ◽  
pp. 946-949
Author(s):  
Jing Fang ◽  
Ruo Xun Zhang
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Lyapunov Stability ◽  
Differential Inequality ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Feedback ◽  
Simulation Results

This paper investigates the synchronization of incommensurate fractional-order chaotic systems, and proposes a modified adaptive-feedback controller for fractional-order chaos synchronization based on Lyapunov stability theory, fractional order differential inequality and adaptive control theory. This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way. Simulation results for a fractional-order chaotic system is provided to illustrate the effectiveness of the proposed scheme.

A SIMPLE SYNCHRONIZATION SCHEME OF GENESIO–TESI SYSTEM BASED ON THE BACK-STEPPING DESIGN

2014 ◽  
Vol 28 (05) ◽  
pp. 1450012 ◽  
Author(s):  
ZUOLEI WANG ◽  
YAOLIN JIANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Convergence Speed ◽  
Control Coefficient ◽  
State Variable ◽  
Synchronization Scheme

Synchronization of the Genesio–Tesi chaotic system is investigated via back-stepping method. Based on the Lyapunov stability theory, a novel scheme is designed. A global asymptotical synchronization can be realized via two simpler controllers, each controller involving only one state variable. Furthermore, the convergence speed can be adjusted by control coefficient. Finally, some numerical simulations are employed to verify the effectiveness of the proposed methods.

Chaos control of the power system via sliding mode based on fuzzy supervisor

2017 ◽  
Vol 10 (1) ◽  
pp. 68-79 ◽  
Author(s):  
Ahmad Sarani Ali Abadi ◽  
Saeed Balochian
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Closed Loop ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Content Type ◽  
Mode Control ◽  
Fuzzy Supervisor

Purpose The purpose of this paper is to address the problem of control in a typical chaotic power system. Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers. So, the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system, eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures. Design/methodology/approach The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory. Findings Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system, eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures. Originality/value Main contributions of the paper are as follows: the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed; designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time; while the generator speed is constant, the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time; stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory; simulation of the proposed controller shows that the chattering is low control signal.

Robust adaptive sliding mode control for a human-driven knee joint orthosis

2018 ◽  
Vol 45 (3) ◽  
pp. 379-389 ◽  
Author(s):  
Rihab Bkekri ◽  
Anouar Benamor ◽  
Mohamed Amine Alouane ◽  
Georges Fried ◽  
Hassani Messaoud
Keyword(s):  
Knee Joint ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Content Type ◽  
Adaptive Sliding Mode ◽  
Robust Adaptive

Purpose Assistive technology products are designed to provide additional accessibility to individuals who have physical or cognitive difficulties, impairments and disabilities. The purpose of this paper is to deal with the control of a knee joint orthosis intended to be used for rehabilitation and assistive purpose; this control aims to reduce the influence of the uncertainties and eliminating the external disturbances in the system. Design/methodology/approach This paper deals with the robust adaptive sliding mode controller (ASMC) of human-driven knee joint orthosis system with mismatched uncertainties and external disturbances. The shank-orthosis system has been modeled and its parameters have been identified. This control reduces the effect of parameter uncertainties and external disturbances on the system performance and improves the system robustness as results. The ASMC was designed to offer the possibility to track the state of the reference model. Moreover, the Lyapunov stability theory was used to study the asymptotical stability of the ASMC. Findings The advantage of the robust ASMC method is the tracking precision and reducing the required time for eliminating external disturbances and uncertainties. The experimental results show in real-time in terms of stability and present that the advantages of this control approach are the position tracking and robustness. Originality/value In this paper, to deal with the parameter uncertainties of the human-driven knee joint orthosis, an ASMC was successfully applied based on sliding mode and Lyapunov stability theory. It has good dynamic response and tracking performance. Besides, the adaptive algorithm is simple, easy to achieve and has good adaptability and robustness against the parameter variations and external disturbances. The design technique is simple and efficient. The development of this control takes into consideration the perturbation, allowing to track a desired trajectory.

Synchronization of the Modified Financial Chaotic System via a Single Controller

2011 ◽  
Vol 230-232 ◽  
pp. 1045-1048
Author(s):  
Jun Li ◽  
Cheng Rong Xie
Keyword(s):  
Linear Matrix Inequality ◽  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Single Controller ◽  
Dynamical Properties

This paper introduces a modified financial chaotic system. Some basic dynamical properties are studied. Based on Lyapunov stability theory and LMI (linear matrix inequality), sufficient condition for the synchronization has been analyzed theoretically. Numerical simulations are given to show the effectiveness of this method.

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