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.

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.

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.

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.

SYNCHRONIZATION BETWEEN TWO DIFFERENT HYPERCHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2013 ◽  
Vol 27 (13) ◽  
pp. 1350044
Author(s):  
XING-YUAN WANG ◽  
YU-HONG YANG ◽  
MING-KU FENG
Keyword(s):  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme.

Exponential synchronization and anti-synchronization of nonautonomous chaotic systems with uncertain parameters via adaptive control

2020 ◽  
Vol 31 (10) ◽  
pp. 2050137
Author(s):  
Xuefei Chen ◽  
Bingyue Liu ◽  
Huizhao Liu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Exponential Synchronization ◽  
Uncertain Parameters ◽  
Adaptive Laws ◽  
Error System ◽  
Analytic Expression

The exponential synchronization and anti-synchronization of nonautonomous chaotic systems with uncertain parameters are studied. The adaptive controller is designed and analytic expression of the controller and the adaptive laws of parameters are given. Based on the Lyapunov stability theory, the exponential stability of the error system is proved. Numerical simulations of two nonautonomous chaotic systems with uncertain parameters are presented to illustrate the ability and effectiveness of the proposed method.

Adaptive Control of Chaotic Systems with Uncertainties

1998 ◽  
Vol 08 (10) ◽  
pp. 2041-2046 ◽  
Author(s):  
Huaizhou Zhang ◽  
Huashu Qin ◽  
Guanrong Chen
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Radial Basis Function Network ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Control Scheme ◽  
On Line ◽  
Uncertain Chaotic Systems ◽  
Adaptation Law ◽  
Function Network

In this paper, an adaptive control scheme, that employs a Gaussian radial basis function network with output weights updated on-line according to the Lyapunov stability theory, is suggested for regulation of a class of chaotic systems with uncertainties. Theoretical analysis guarantees that under the control of the proposed adaptation law, uncertain chaotic systems can asymptoticaly track target orbits within arbitrarily small tolerance bounds. As an example, control of the uncertain Duffing–Holmes system is presented with computer simulations, which verifies and visualizes the theory and design of the adaptive controller.

scholarly journals A Novel Scheme Adaptive Hybrid Dislocated Synchronization for Two Identical and Different Memristor Chaotic Oscillator Systems with Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Chen ◽  
Junwei Sun ◽  
Ming Chi ◽  
Xin-Ming Cheng
Keyword(s):  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Parameters Estimation ◽  
Drive System ◽  
Projective Synchronization ◽  
Chaotic Oscillator ◽  
Uncertain Parameters ◽  
State Variables ◽  
Response System

The drive system can synchronize with the response system by the scaling factor in the traditional projective synchronization. This paper proposes a novel adaptive hybrid dislocated synchronization with uncertain parameters scheme for chaos synchronization using the Lyapunov stability theory. The drive system is synchronized by the sum of hybrid dislocated state variables for the response system. By designing effective hybrid dislocated adaptive controller and hybrid dislocated adaptive law of the parameters estimation, we investigate the synchronization of two identical memristor chaotic oscillator systems and two different memristor chaotic oscillator systems with uncertain parameters. Finally, the numerical simulation examples are provided to show the effectiveness of our method.

Logic-Based Switching Adaptive Control of DC-DC Buck Converter

2012 ◽  
Vol 229-231 ◽  
pp. 2209-2212
Author(s):  
Bao Bin Liu ◽  
Wei Zhou
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Buck Converter ◽  
Uncertain Parameters ◽  
Small Signal ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
Signal Model ◽  
Small Signal Model ◽  
Control Scheme

Logic-based switching adaptive control scheme is proposed for the model of DC-DC buck converter in presence of uncertain parameters and power supply disturbance. All uncertain parameters and the disturbance are estimated together through constructing Lyapunov function. And a switching mechanism is used to ensure global asymptotic stability of the closed-loop system. The results of simulation show that even if there are multiple unknown parameters in the small-signal model, the control system of DC-DC buck converter can estimate unknown parameters quickly and accurately.

scholarly journals Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shih-Yu Li ◽  
Cheng-Hsiung Yang ◽  
Li-Wei Ko ◽  
Chin-Teng Lin ◽  
Zheng-Ming Ge
Keyword(s):  
Adaptive Control ◽  
Stability Theory ◽  
Initial Conditions ◽  
Stability Theorem ◽  
Phase Portraits ◽  
Adaptive Synchronization ◽  
Complex Signal ◽  
Uncertain Parameters ◽  
Chaotic Motions ◽  
Lorentz System

We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the similar chaotic signal of time-reversed Lorentz system. In addition, pragmatical asymptotically stability theorem and an assumption of equal probability for ergodic initial conditions (Ge et al., 1999, Ge and Yu, 2000, and Matsushima, 1972) are proposed to strictly prove that adaptive control can be accomplished successfully. The current scheme of adaptive control—by traditional Lyapunov stability theorem and Barbalat lemma, which are used to prove the error vector—approaches zero, as time approaches infinity. However, the core question—why the estimated or given parameters also approach to the uncertain parameters—remains without answer. By the new stability theory, those estimated parameters can be proved approaching the uncertain values strictly, and the simulation results are shown in this paper.

A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 205-210 ◽  
Author(s):  
An-Chyau Huang ◽  
Shi-Chang Wu ◽  
Wen-Fa Ting
Keyword(s):  
Function Approximation ◽  
Matrix Theory ◽  
Robot Manipulator ◽  
Nonlinear Differential Equations ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Control Scheme ◽  
Approximation Errors ◽  
Theory And Experiments

In this paper, an adaptive control scheme is proposed for an n-link rigid robot manipulator without using the regressor. The robot is firstly modeled as a set of second-order nonlinear differential equations with the assumption that all of the matrices in that model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique (FAT) is used here to represent uncertainties in some finite linear combinations of orthonormal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. Experiments are also performed on a 2-D robot to test the efficacy of the proposed scheme.

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