Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa ◽  
Bijan Hashtarkhani
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
Uncertain Chaotic Systems ◽  
The Stability ◽  
Feedback Control Strategy ◽  
Adaptive Control Scheme

In this paper, an adaptive control scheme is offered to synchronize two different uncertain chaotic systems. It is assumed that the whole dynamics of both master and slave chaotic systems and their bounds are unknown and different. The error system stabilization is achieved in two cases: with input nonlinearities and without input nonlinearities. We design an adaptive control scheme based on the state boundedness property of the chaotic systems. The proposed method does not need any information about nonlinear/linear terms of the chaotic systems. It only uses an adaptive feedback control strategy. The stability of the proposed controllers is proved by using the Lyapunov stability theory. Finally, the designed adaptive controllers are applied to synchronize two different pairs of the chaotic systems (Lorenz–Chen and electromechanical device–electrostatic transducer).

Adaptive Control of Hyper-Chaotic Systems Based on Dynamic Structure RBF Neural Networks

2012 ◽  
Vol 229-231 ◽  
pp. 2311-2314
Author(s):  
Jing Wang ◽  
Hong Xia Gao ◽  
Zhen Yu Tan ◽  
Jin Feng Gao
Keyword(s):  
Neural Networks ◽  
Adaptive Control ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Dynamic Structure ◽  
Rbf Neural Networks ◽  
Closed Loop System ◽  
Control Scheme ◽  
The Stability ◽  
Adaptive Control Scheme

An adaptive control scheme based on neural networks is presented for control of hyper-chaotic systems. Parameters of neural networks and controllers are adjusted automatically to ensure the stability of the closed-loop system. Numerical simulation illustrates that the proposed control scheme is valid for hyper-chaotic system.

SYNCHRONIZING CASCADE-CONNECTED CHAOTIC SYSTEMS WITH UNCERTAINTIES AND BREAKING CHAOTIC CRYPTOSYSTEMS VIA A NOVEL ADAPTIVE CONTROL SCHEME

2005 ◽  
Vol 15 (08) ◽  
pp. 2457-2468 ◽  
Author(s):  
JUHNG-PERNG SU ◽  
CHUN-CHIEH WANG
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Synthesis Method ◽  
Robust Adaptive Control ◽  
Barbalat’S Lemma ◽  
Control Scheme ◽  
Master System ◽  
Adaptive Control Scheme

This paper deals with synchronization problems of chaotic systems by applying a new adaptive variable structure control (AVSC) scheme. On the basis of Lyapunov synthesis method and Barbalat's Lemma, the proposed control law is shown to render the slave system asymptotically synchronized with the master system even though the parameters of the master system are unknown. A robust adaptive control scheme is presented to guarantee the robustness of the synchronization against bounded disturbances. Even for the case that the slave and master chaotic systems are not of the same type, the proposed AVSC may approximately null the synchronization error. We used an uncertain Rössler system, an uncertain Chua's circuit and an uncertain Duffing–Holmes oscillator as examples to illustrate the controller design. Both theoretical and simulation results strongly suggest that chaotic cryptosystems could be broken by the proposed adaptive control method. This reveals the fact that chaos-based cryptosystems may fail to achieve the secure communication.

Cluster synchronization in fractional-order network with nondelay and delay coupling

2021 ◽  
pp. 2250006
Author(s):  
Yi Wang ◽  
Zhaoyan Wu
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Cluster Synchronization ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability ◽  
Adaptive Control Scheme

In this paper, cluster synchronization for fractional-order complex network with nondelay and delay coupling is investigated. Based on the stability theory of fractional-order systems and the properties of fractional derivative, both static and adaptive control schemes are adopted to design effective controllers. Sufficient condition for achieving cluster synchronization about static controllers is provided. From the condition, the needed feedback gains can be estimated by simple calculations. Further, adaptive control scheme is introduced to design unified controllers. Noticeably, in the adaptive controllers, the feedback gains need not be calculated in advance and can adjust themselves to the needed values according to updating laws. Finally, numerical simulations are given to demonstrate the correctness of the obtained results.

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 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 A Distributed Autonomous Control Method for TCUL Transformers Using a Fuzzy Adaptive Control Scheme

1999 ◽  
Vol 119 (12) ◽  
pp. 1455-1461 ◽  
Author(s):  
Naoto Yorino ◽  
Takanori Shuto ◽  
Masaomi Nishimoto ◽  
Hiroshi Sasaki ◽  
Hiroaki Sugihara ◽  
...  
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Autonomous Control ◽  
Fuzzy Adaptive Control ◽  
Control Scheme ◽  
Adaptive Control Scheme ◽  
Fuzzy Adaptive

Projective lag synchronization in drive-response dynamical networks

2014 ◽  
Vol 25 (11) ◽  
pp. 1450068 ◽  
Author(s):  
Ghada Al-Mahbashi ◽  
Mohd Salmi Md Noorani ◽  
Sakhinah Abu Bakar
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
Feedback Control Method ◽  
Projective Lag Synchronization ◽  
Error Dynamics ◽  
The Stability

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

scholarly journals Composite adaptive control of a robotic joint for passive deployment applications

2002 ◽  
Vol 216 (3) ◽  
pp. 275-289
Author(s):  
A V C Reedman ◽  
K Bouazza-Marouf
Keyword(s):  
Adaptive Control ◽  
Control Strategies ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
And Control ◽  
The Mathematical Model ◽  
Composite Adaptive Control ◽  
Single Worm ◽  
Adaptive Control Scheme ◽  
Computed Torque

A composite adaptive control scheme for the control of an actively constrained revolute joint with backlash cancellation is presented in this paper. The drive mechanism consists of two motor-driven worms coupled to a single worm wheel. The mathematical model and control strategies are reviewed. This is followed by the derivation of the composite adaptive controllers. Simulation and experimental results show that the composite adaptive control scheme gives an equivalent performance to a computed-torque algorithm without compromising the mechanism's ability to cancel backlash.

Complex Hybrid Synchronization in Drive-Response Complex-Variable Chaotic Systems

2012 ◽  
Vol 13 (7-8) ◽  
Author(s):  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Scheme ◽  
Hybrid Synchronization ◽  
Complex Hybrid ◽  
First Time ◽  
In Virtue Of ◽  
Response Complex

AbstractIn this paper, the concept of complex hybrid synchronization in complex-variable chaotic system is introduced for the first time. Based on Lyapunov stability theory, two typical complex-variable chaotic systems are considered and corresponding controllers are designed to achieve complex hybrid synchronization. Further, a universal control method in virtue of adaptive control scheme is proposed. Numerical examples are provided to show the effectiveness of the proposed method.

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