SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC AND CHAOTIC SYSTEMS BY ADAPTIVE CONTROL

2008 ◽  
Vol 18 (12) ◽  
pp. 3731-3736 ◽  
Author(s):  
ZHI-YU LIU ◽  
CHIA-JU LIU ◽  
MING-CHUNG HO ◽  
YAO-CHEN HUNG ◽  
TZU-FANG HSU ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Mean Squared Error ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Slave System ◽  
Unknown Parameters ◽  
Squared Error ◽  
Master System ◽  
Two Systems ◽  
The Mean

This paper presents the synchronization between uncertain hyperchaotic and chaotic systems. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of hyperchaotic and chaotic systems, including the case of unknown parameters in these two systems. The T.N.Č. hyperchaotic oscillator is used as the master system, and the Rössler system is used as the slave system. Numerical simulations verify these results. Additionally, the effect of noise is investigated by measuring the mean squared error (MSE) of two systems.

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.

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.

Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach

2012 ◽  
Vol 1 (3) ◽  
pp. 122-138 ◽  
Author(s):  
G. El-Ghazaly
Keyword(s):  
Fuzzy Systems ◽  
Chaotic Systems ◽  
Small Neighborhood ◽  
Lyapunov Stability Theory ◽  
Approximate Model ◽  
Adaptive Synchronization ◽  
Control Input ◽  
Slave System ◽  
Master System ◽  
Unknown Chaotic Systems

The synchronization problem for a general-class of unknown chaotic systems is addressed. Fuzzy systems in Mamdani type are employed to provide an approximate model of the master chaotic system using an adaptive approach. Within this, a number of fuzzy systems are utilized to approximate the unknown nonlinear functions of the master system. An approximate model similar to the master system is constructed which is the slave system. The error dynamics between the master and slave chaotic systems is used to build a suitable control input and fuzzy systems’ parameters adaptive laws to force the slave system to be synchronized with master system. The stability of the overall synchronization system is derived based on Lyapunov stability theory. Its shown that under appropriate assumptions, the proposed approach guarantees the boundness and asymptotic convergence of synchronization errors to a small neighborhood of origin. An extensive simulation study is performed on both Duffing and Rössler chaotic systems to show the effectiveness of the proposed scheme.

scholarly journals Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control

2011 ◽  
Vol 2 (1) ◽  
pp. 17-28
Author(s):  
Vaidyanathan SUNDARAPANDIAN ◽  
Karthikeyan RAJAGOPAL
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Uncertain Chaotic Systems

In this paper, we apply adaptive control method toderive new results for the anti-synchronization of identical Tigansystems (2008), identical Li systems (2009) and non-identical Tiganand Li systems. In adaptive anti-synchronization of identical chaoticsystems, the parameters of the master and slave systems are unknownand we devise feedback control law using the estimates of the systemparameters. In adaptive anti-synchronization of non-identical chaoticsystems, the parameters of the master system are known, but theparameters of the slave system are unknown and we devise feedbackcontrol law using the estimates of the parameters of the slave system.Our adaptive synchronization results derived in this paper for theuncertain Tigan and Li systems are established using Lyapunovstability theory. Since the Lyapunov exponents are not required forthese calculations, the adaptive control method is very effective andconvenient to achieve anti-synchronization of identical and nonidenticalTigan and Li systems. Numerical simulations are shown todemonstrate the effectiveness of the adaptive anti-synchronizationschemes for the uncertain chaotic systems addressed in this paper.

scholarly journals Die Robustheit von BLUP und EBLUP

1999 ◽  
Vol 42 (3) ◽  
pp. 303-318
Author(s):  
G. Herrendörfer ◽  
A. Tuchscherer ◽  
G. Dietl ◽  
M. Tuchscherer
Keyword(s):  
Computer Simulation ◽  
Variance Components ◽  
Fixed Effects ◽  
Variance Component ◽  
Mean Squared Error ◽  
Unknown Parameters ◽  
Selection Gain ◽  
Squared Error ◽  
Random Components ◽  
The Mean

Abstract. Title of the paper: The Robustness of BLUP and EBLUP The expectations of BLP and BLUP used as estimator for fixed effects and as predictor for random effects were investigated concerning the property "unbiasedness". Different aspects of robustness research on prediction procedures are discussed. The robustness of BLUP and EBLUP was investigated with respect to the distribution ofthe random components of the model, the degree of balancedness of the experimental design, influence of the variance components ratio and different variance component estimators used in EBLUP(2) on the bases of a Computer Simulation in the random one-way model. Criteria used for the evaluation were the mean squared error (MSE) and the selection gain. Besides, an idea of the overestimation of the accuracy of EBLUP by the naive MSE approximation based on the MSE formulas of BLUP with variance component estimations instead of unknown parameters is given.

Computing trade-offs in robust design: Perspectives of the mean squared error

2011 ◽  
Vol 60 (2) ◽  
pp. 248-255 ◽  
Author(s):  
Sangmun Shin ◽  
Funda Samanlioglu ◽  
Byung Rae Cho ◽  
Margaret M. Wiecek
Keyword(s):  
Robust Design ◽  
Mean Squared Error ◽  
Squared Error ◽  
Trade Offs ◽  
The Mean

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

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