scholarly journals Adaptive Synchronization for Hyperchaotic Liu System

2022 ◽  
Vol 9 ◽  
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Gang Zheng
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Control Schemes ◽  
Liu System ◽  
Adaptive Control Law

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

scholarly journals Adaptive Anti-synchronization of Identical and Non-identical 4-D Chaotic Systems

2012 ◽  
pp. 160-164
Author(s):  
H. Najafizadegan ◽  
M. Khoeiniha ◽  
H. Zarabadipour
Keyword(s):  
Adaptive Control ◽  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Unknown Parameters ◽  
Different Chaotic Systems ◽  
Adaptive Control Law

In this paper, we investigate the chaos anti-synchronization between two identical and different chaotic systems with fully unknown parameters via adaptive control. Based on the Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are designed such that the two different chaotic systems can be anti-synchronized asymptotically. Theoretical analysis and numerical simulations are shown to verify the results.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

2017 ◽  
Vol 6 (4) ◽  
pp. 1-16 ◽  
Author(s):  
A. Almatroud Othman ◽  
M.S.M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

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.

Adaptive Control of Robot Manipulators Including Motor Dynamics

1995 ◽  
Vol 209 (3) ◽  
pp. 207-217
Author(s):  
H Yu ◽  
S Lloyd
Keyword(s):  
Adaptive Control ◽  
Control Structure ◽  
Robot Manipulators ◽  
Control Law ◽  
Task Space ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability ◽  
Adaptive Control Law ◽  
Motor Dynamics

An adaptive control scheme for robot manipulators including motor dynamics is proposed in this paper. The proposed scheme avoids the assumption that the values of motor parameters are known which is required in reference (13). An exponential control law is first developed under the assumption of no uncertainty. This forms a controller structure for the adaptive control. Using this control structure, a full-order adaptive control law is proposed to overcome parameter uncertainty for both robot link and motor. The stability analysis is in the Lyapunov stability sense. The method is further extended to the task space. Extensive simulations are performed to compare the different control schemes.

scholarly journals Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Paul Yaovi Dousseh ◽  
Cyrille Ainamon ◽  
Clément Hodévèwan Miwadinou ◽  
Adjimon Vincent Monwanou ◽  
Jean Bio Chabi Orou
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Stability Theory ◽  
Financial System ◽  
Adaptive Synchronization ◽  
Control Law ◽  
State Variables ◽  
Unknown Constant ◽  
Theoretical Results ◽  
Adaptive Control Law

In this paper, adaptive control and adaptive synchronization of an integer and fractional order new financial system with unknown constant parameters are studied. Based on Lyapunov’s stability theory, an adaptive control law is designed to asymptotically stabilize the state variables of the system to the origin in integer and fractional order cases. By the same theory, an adaptive synchronization law is designed to perform the identical synchronization of the new financial system in the cases of integer and fractional order with unknown constant parameters. Numerical simulations are carried out in order to show the efficiency of the theoretical results.

scholarly journals Adaptive Synchronization in Complex Network with Different Order Node Dynamics

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fan-di Zhang ◽  
Jin-ping Jia ◽  
Li-xin Yang
Keyword(s):  
Adaptive Control ◽  
Complex Networks ◽  
Complex Network ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Cluster Synchronization ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Different Order

This paper investigates the adaptive cluster synchronization in the complex networks with different orders. By means of Lyapunov stability theory and the adaptive control technique, a novel adaptive synchronization controller is developed. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyperchaotic node dynamics are presented.

scholarly journals Generalized Synchronization with Uncertain Parameters of Nonlinear Dynamic System via Adaptive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cheng-Hsiung Yang ◽  
Cheng-Lin Wu
Keyword(s):  
Adaptive Control ◽  
Dynamic Systems ◽  
Chaos Synchronization ◽  
Chaotic Dynamic ◽  
Nonlinear Dynamic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Control Scheme

An adaptive control scheme is developed to study the generalized adaptive chaos synchronization with uncertain chaotic parameters behavior between two identical chaotic dynamic systems. This generalized adaptive chaos synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the adaptive controller with its update laws of uncertain chaotic parameters is shown. The generalized adaptive synchronization with uncertain parameters between two identical new Lorenz-Stenflo systems is taken as three examples to show the effectiveness of the proposed method. The numerical simulations are shown to verify the results.

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