Application of Synchronization Control Method to Zagzag System

2012 ◽  
Vol 241-244 ◽  
pp. 1067-1070
Author(s):  
Yin Li ◽  
Chun Long Zheng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Control Method ◽  
Stability Theorem ◽  
Synchronization Control ◽  
Lyapunov Stability Theorem ◽  
Synchronization Scheme

In this paper, synchronization control method of Zagzag system is discussed both theoretically and numerically. Based on the Lyapunov stability theorem and the chaotic methods, synchronization control is given and illustrated with Zagzag system as example. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization scheme.

Synchronization and Anti-Synchronization of the Chaotic Modified Chua's Circuits via a Same Controller

2012 ◽  
Vol 605-607 ◽  
pp. 1972-1975
Author(s):  
Jian Cai Leng ◽  
Rong Wei Guo
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Global Synchronization ◽  
Single Input ◽  
Theoretical Results

Based on the Lyapunov stability theorem, a same controller in the form is designed to achieve the global synchronization and anti-synchronization of the chaotic modified Chua's circuits. The controller obtained in this paper is simpler than those obtained in the existing results, and it is a linear single input controller. Numerical simulations verify the correctness and the effectiveness of the proposed theoretical results

scholarly journals Synchronization and Lag Synchronization of Hyperchaotic Memristor-Based Chua’s Circuits

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Hui Wang ◽  
Xin Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Chua’S Circuit ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Chua's Circuit ◽  
Initial Values ◽  
Theoretical Results

A memristor-based five-dimensional (5D) hyperchaotic Chua’s circuit is proposed. Based on the Lyapunov stability theorem, the controllers are designed to realize the synchronization and lag synchronization between the hyperchaotic memristor-based Chua’s circuits under different initial values, respectively. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

GENERALIZED PROJECTIVE SYNCHRONIZATION OF A CLASS OF DELAYED NEURAL NETWORKS

2008 ◽  
Vol 22 (03) ◽  
pp. 181-190 ◽  
Author(s):  
JUAN MENG ◽  
XINGYUAN WANG
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Generalized Projective Synchronization

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

Stability Analysis of a Flexible Two-Link Timoshenko Manipulator Using Boundary Control Method

2008 ◽  
Author(s):  
Hossein Rastgoftar ◽  
Masih Mahmoodi ◽  
Mohammad Eghtesad ◽  
Mojtaba Kazemi
Keyword(s):  
Stability Analysis ◽  
Boundary Control ◽  
Lyapunov Stability ◽  
Timoshenko Beam ◽  
Control Method ◽  
Beam Theory ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Stabilization Problem ◽  
Boundary Control Method

In this article, the stabilization problem of two flexible one-link and two-link manipulators is solved using boundary control method. To account for the flexibility of links, Timoshenko beam theory is adopted and using Lyapunov stability theorem, forces and torques necessary to be applied at the joints of the manipulators are calculated. Finally the problem of trajectory tracking for this robot is briefly discussed.

scholarly journals Hybrid Dislocated Control and General Hybrid Projective Dislocated Synchronization for Memristor Chaotic Oscillator System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Junwei Sun ◽  
Chun Huang ◽  
Guangzhao Cui
Keyword(s):  
Control Method ◽  
Stability Theorem ◽  
The Other ◽  
Chaotic Oscillator ◽  
Lyapunov Stability Theorem ◽  
Oscillator System ◽  
Different Dimensions ◽  
Unstable Equilibrium Point ◽  
Dynamical Properties ◽  
Synchronization Scheme

Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic oscillator system. For the different dimensions, the memristor chaotic oscillator system and the other chaotic system have realized general hybrid projective dislocated synchronization. Numerical simulations are given to show the effectiveness of these methods.

ANTI-SYNCHRONIZATION OF A CLASS OF COUPLED CHAOTIC SYSTEMS VIA LINEAR FEEDBACK CONTROL

2006 ◽  
Vol 16 (04) ◽  
pp. 1041-1047 ◽  
Author(s):  
CHUANDONG LI ◽  
XIAOFENG LIAO
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Feedback ◽  
Generalized Synchronization ◽  
Lyapunov Stability Theorem ◽  
Linear Feedback Control ◽  
Relevant Variables ◽  
Special Case

As a special case of generalized synchronization, chaos anti-synchronization can be characterized by the vanishing of the sum of relevant variables. In this paper, based on Lyapunov stability theorem for ordinary differential equations, several sufficient conditions for guaranteeing the existence of anti-synchronization in a class of coupled identical chaotic systems via linear feedback or adaptive linear feedback methods are derived. Chua's circuit is presented as an example to demonstrate the effectiveness of the proposed approach by computer simulations.

Switched Projective Synchronization of the Stochastic Newton-Leipnik System

2013 ◽  
Vol 328 ◽  
pp. 570-574
Author(s):  
Duan Dong ◽  
Shao Juan Ma ◽  
Jie Zheng
Keyword(s):  
Hilbert Spaces ◽  
Chaotic Systems ◽  
Control Method ◽  
Random Parameter ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Deterministic System ◽  
Lyapunov Stability Theorem ◽  
Orthogonal Polynomial Expansion

The paper is involved with switched projective synchronization of two identical chaotic systems with random parameter using adaptive control method. Based on the orthogonal polynomial expansion of the Hilbert spaces, the Newton-Leipnik system with random parameter is transformed as the equivalent deterministic system. At last, an adaptive controller can be designed by the Lyapunov stability theorem for achieving switched projective synchronization of the equivalent deterministic system with different initial values. Corresponding numerical simulations are performed to verify the effectiveness of presented schemes for synchronizing the stochastic Newton-Leipnik system.

scholarly journals Lyapunov Stability Analysis of Gradient Descent-Learning Algorithm in Network Training

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Ahmad Banakar
Keyword(s):  
Lyapunov Stability ◽  
Gradient Descent ◽  
Learning Algorithm ◽  
Stability Theorem ◽  
Stability And Convergence ◽  
Lyapunov Stability Theorem ◽  
Network Training ◽  
Learning Rates ◽  
Lyapunov Stability Analysis ◽  
The Stability

The Lyapunov stability theorem is applied to guarantee the convergence and stability of the learning algorithm for several networks. Gradient descent learning algorithm and its developed algorithms are one of the most useful learning algorithms in developing the networks. To guarantee the stability and convergence of the learning process, the upper bound of the learning rates should be investigated. Here, the Lyapunov stability theorem was developed and applied to several networks in order to guaranty the stability of the learning algorithm.

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