AN ADAPTIVE OBSERVER DESIGN FOR AUTO-SYNCHRONIZATION OF LORENZ SYSTEM

2008 ◽  
Vol 18 (08) ◽  
pp. 2415-2423 ◽  
Author(s):  
YING LIU ◽  
WALLACE TANG ◽  
LJUPCO KOCAREV
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Observer Design ◽  
Adaptive Observer ◽  
Simple Design ◽  
Unknown Parameters ◽  
Dynamical Equations ◽  
Design Rules ◽  
The Past

Synchronization of chaotic systems with unknown parameters, or namely auto-synchronization, has aroused a lot of interest in the past few years. In this paper, we are interested in solving one of the critical cases in Lorenz system. Based on the past researches, it was concluded that the auto-synchronization of Lorenz system was inachievable if the unknown parameters resided in all of its three dynamical equations while only the first state was measurable. However, as demonstrated in this paper, this problem can be resolved by an adaptive observer following simple design rules. The design is justified with the conditional Lyapunov exponents, and its effectiveness is clearly illustrated in simulations.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

Adaptive full-order and reduced-order observers for one-sided Lur'e systems with set-valued mappings

2016 ◽  
Vol 35 (2) ◽  
pp. 569-589 ◽  
Author(s):  
Min-Jie Shi ◽  
Jun Huang ◽  
Liang Chen ◽  
Lei Yu
Keyword(s):  
Differential Inclusion ◽  
Design Method ◽  
Rotor System ◽  
Observer Design ◽  
Adaptive Observer ◽  
Unknown Parameters ◽  
Lur’E Systems ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Set Valued Mappings

AbstractThis article proposes an adaptive observer design method for one-sided Lipschitz Lur'e differential inclusion systems with unknown parameters. First, under some assumptions, we design an adaptive full-order observer for the system. Then, under the same assumptions, a reduced-order observer is proved to be valid. Finally, we simulate an example to show the effectiveness of the presented method under the background of rotor system.

GENERALIZED SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS BASED ON PARAMETER IDENTIFICATION

2009 ◽  
Vol 23 (22) ◽  
pp. 2593-2606 ◽  
Author(s):  
YONGGUANG YU ◽  
HAN-XIONG LI ◽  
JUNZHI YU
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Generalized Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Response System ◽  
Generalized Lorenz System ◽  
The One

This paper investigates the generalized synchronization issue for two different dimensional chaotic systems with unknown parameters. Based on Lyapunov stability theory and adaptive control theory, an adaptive controller is derived to achieve the generalized synchronization whether the dimension of drive system is greater than the one of the response system or not. Meanwhile, corresponding parameter updating laws can be obtained so as to exactly identify uncertain parameters. This technique has been successfully applied to two examples, the generalized synchronization of hyperchaotic Rössler system and chaotic Lorenz system, chaotic Chen system and generalized Lorenz system. Numerical simulations are finally shown to illustrate the effectiveness of the proposed approach.

Robust H∞ gain neuro-adaptive observer design for nonlinear uncertain systems

2018 ◽  
Vol 41 (8) ◽  
pp. 2293-2309
Author(s):  
Krifa Abdelkader ◽  
Bouzrara Kais
Keyword(s):  
Nonlinear Approximation ◽  
The State ◽  
Observer Design ◽  
Adaptive Observer ◽  
Projection Algorithm ◽  
Linear Matrix ◽  
Positive Real ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Persistent Excitation

To guarantee convergent state estimates and exact approximations, it is highly desirable that observers can independently dominate the effects of unmodelled dynamics. Based on adaptive nonlinear approximation, this paper presents a robust H∞ gain neuro-adaptive observer (R H∞GNAO) design methodology for a large class of uncertain nonlinear systems in the presence of time-varying unknown parameters with bounded external disturbances on the state vector and on the output of the original system. The proposed R H∞GNAO incorporates radial basis function neural networks (RBFNNs) to approximate the unknown nonlinearities in the uncertain system. The weight dynamics of every RBFNN are adjusted online by using an adaptive projection algorithm. The asymptotic convergence of the state and parameter estimation errors is achieved by using Lyapunov cogitation under a well-defined persistent excitation condition, and without recourse to the strictly positive real condition. The repercussions of unknown disturbances are reduced by integrating an H∞ gain performance criterion into the proposed estimation approach. The condition imposed by this proposed observer approach, such that all estimated signals are uniformly ultimately bounded, is expressed in the form of the linear matrix inequality problem and warrants the demanded performances. To evaluate the performance of the proposed observer, various simulations are presented.

Synchronization of Quadratic Chaotic Systems Based on Simultaneous Estimation of Nonlinear Dynamics

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Amin Zarei ◽  
Saeed Tavakoli
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Simultaneous Estimation ◽  
Control Law ◽  
Adaptive Mechanism ◽  
Lyapunov Theorem ◽  
Unknown Parameters ◽  
The Lorenz System ◽  
Synchronization Scheme

To synchronize quadratic chaotic systems, a synchronization scheme based on simultaneous estimation of nonlinear dynamics (SEND) is presented in this paper. To estimate quadratic terms, a compensator including Jacobian matrices in the proposed master–slave schematic is considered. According to the proposed control law and Lyapunov theorem, the asymptotic convergence of synchronization error to zero is proved. To identify unknown parameters, an adaptive mechanism is also used. Finally, a number of numerical simulations are provided for the Lorenz system and a memristor-based chaotic system to verify the proposed method.

ADAPTIVE OBSERVER-BASED SYNCHRONIZATION FOR COMMUNICATION

2000 ◽  
Vol 10 (12) ◽  
pp. 2807-2813 ◽  
Author(s):  
ALEXANDER FRADKOV ◽  
HENK NIJMEIJER ◽  
ALEXEY MARKOV
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Signal Transmission ◽  
Adaptive Observer ◽  
Simple Design ◽  
Quadratic Lyapunov Function ◽  
Unknown Parameters ◽  
Error System

The problem of synchronizing two nonlinear systems (transmitter and receiver) is considered. A simple design of an adaptive observer for estimating the unknown parameters of the transmitter is proposed based on the design of quadratic Lyapunov function for the error system. The results are illustrated by an example of signal transmission based on a pair of synchronizing Chua circuits.

scholarly journals Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Unknown Parameters ◽  
Integer Order ◽  
System A ◽  
Control Scheme ◽  
Lorenz Chaotic System

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

Synchronization of chaotic systems based on adaptive observer design

2004 ◽  
Vol 13 (9) ◽  
pp. 1391-1395 ◽  
Author(s):  
Hua Chang-Chun ◽  
Guan Xin-Ping
Keyword(s):  
Chaotic Systems ◽  
Observer Design ◽  
Adaptive Observer

Nonlinear Adaptive Observer-Based Fault Diagnosis for Satellite Actuator

2012 ◽  
Vol 214 ◽  
pp. 851-855 ◽  
Author(s):  
Zhi Wang
Keyword(s):  
Observer Design ◽  
Adaptive Observer ◽  
Asymptotic Convergence ◽  
Sufficient Condition ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Nonlinear Object ◽  
Adaptive State Observer ◽  
Simulation Results ◽  
Fault Mode

This paper studies the multi-structural fault mode of satellite actuators, and use numbers of unknown parameters as fault indicators. The problem of adaptive state observer design for nonlinear systems with unknown parameters is dealt with by applying Lypunov method. The nonlinear object is firstly linearized into Lipschitz system, and then by analyzing the sufficient condition for asymptotic convergence of the observer, the structure of observer and the adaptive laws for parameter estimation are given. Finally, the adaptive observer is employed to estimate the faults of satellite actuator. Numerical simulation results show that this method is effective and able to quickly detect faults.

Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters

2016 ◽  
Vol 23 (3) ◽  
pp. 389-399 ◽  
Author(s):  
P Bagheri ◽  
M Shahrokhi ◽  
H Salarieh
Keyword(s):  
Chaotic Systems ◽  
Parameters Estimation ◽  
Adaptive Observer ◽  
Nonlinear Observer ◽  
Control Law ◽  
Slave System ◽  
Unknown Parameters ◽  
System Parameters ◽  
Adaptive Laws ◽  
System States

In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is assumed that the parameters of both master and slave systems are unknown. For this case, an adaptive nonlinear observer is designed to estimate the slave system states and two adaptive laws for estimating the unknown parameters are proposed. In addition, a proper control law to achieve the synchronization goal has been suggested, and the stability of the closed-loop system is established. Finally, the effectiveness of the proposed synchronization method is shown via simulation results.

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