scholarly journals Formation Geometry Center based Formation Controller Design using Lyapunov Stability Theorem

2008 ◽  
Vol 9 (2) ◽  
pp. 71-78 ◽  
Author(s):  
Ji-Eun Lee ◽  
Hyeong-Seok Kim ◽  
You-Dan Kim ◽  
KiHoon Han
Keyword(s):  
Lyapunov Stability ◽  
Controller Design ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem

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.

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.

scholarly journals Model Reference Control of Hyperchaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Pengfei Zhao ◽  
Cai Liu ◽  
Xuan Feng
Keyword(s):  
Lyapunov Stability ◽  
Reference System ◽  
Stability Theorem ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
General Description ◽  
Lyapunov Stability Theorem ◽  
Model Reference ◽  
Model Reference Control ◽  
Hyperchaotic Systems

We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for controlling hyperchaotic systems with both certain parameters and uncertain parameters.

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

Sensor-Based Filtering of Stochastic Distributed Parameter Systems

2015 ◽  
Vol 740 ◽  
pp. 229-233
Author(s):  
Wen Ying Mu ◽  
Bao Tong Cui ◽  
Bin Qi
Keyword(s):  
Numerical Simulation ◽  
State Estimation ◽  
Real Time ◽  
Lyapunov Stability ◽  
Adaptive Filters ◽  
Distributed Parameter Systems ◽  
Stability Theorem ◽  
Distributed Parameter ◽  
Evolution System ◽  
Lyapunov Stability Theorem

This Paper Proposes a Scheme for Filtering of Stochastic Distributed Parameter Systems. it is Assumed that a Real-Time Environment Consists of m Groups of Sensors, each of which Provides Necessarily State Spatially Measurements from Sensing Devices. Base on Lyapunov Stability Theorem and Itô formula, a Class of Distributed Adaptive Filters with Penalty Terms Result in the State Errors Forming a Stable Evolution System and Asymptotically Converge to Stochastic Distributed Parameter Systems, and then the Preferable State Estimation is Derived. Numerical Simulation Demonstrates the Effectiveness of the Proposed Method.

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