scholarly journals Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Weiwei Cai ◽  
Xiaomei Cai
Keyword(s):  
Dynamical System ◽  
Parameter Estimation ◽  
State Feedback ◽  
Passive Control ◽  
Adaptive Synchronization ◽  
Passive System ◽  
Unknown Parameters ◽  
Chen System ◽  
Smooth State ◽  
Zero Equilibrium

This paper investigates the synchronization and antisynchronization problems of a hyperchaotic complex Chen system with unknown parameters based on the properties of a passive system. The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. Corresponding parameter estimation update laws are obtained to estimate the unknown parameters as well. Numerical simulations verify the effectiveness of the theoretical analysis.

PASSIVE CONTROL OF HYPERCHAOTIC LORENZ SYSTEM AND CIRCUIT EXPERIMENTAL ON EWB

2007 ◽  
Vol 21 (17) ◽  
pp. 3053-3064 ◽  
Author(s):  
FA-QIANG WANG ◽  
CHONG-XIN LIU
Keyword(s):  
State Feedback ◽  
Passive Control ◽  
Lorenz System ◽  
Control Method ◽  
Equilibrium Points ◽  
Minimum Phase ◽  
Passive System ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaos Control ◽  
Smooth State

Based on the property of a passive system, the essential conditions under which a hyperchaotic Lorenz system could be equivalent to a passive system via smooth state feedback are derived, making the minimum phase hyperchaotic Lorenz system globally asymptotically stabilized at zero and at any desired equilibrium points. The results of simulation on Matlab and the circuit experiment on EWB confirm the effectiveness of the proposed hyperchaos control method.

scholarly journals Adaptive State-Feedback Stabilization for Stochastic Nonholonomic Mobile Robots with Unknown Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenli Feng ◽  
Qingli Sun ◽  
Zhijun Cao ◽  
Dongkai Zhang ◽  
Hua Chen
Keyword(s):  
Mobile Robots ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Unknown Parameters ◽  
Nonholonomic Mobile Robots ◽  
Stabilizing Controllers ◽  
Stochastic Case ◽  
Switching Control Strategy ◽  
Zero Equilibrium

The stabilizing problem of stochastic nonholonomic mobile robots with uncertain parameters is addressed in this paper. The nonholonomic mobile robots with kinematic unknown parameters are extended to the stochastic case. Based on backstepping technique, adaptive state-feedback stabilizing controllers are designed for nonholonomic mobile robots with kinematic unknown parameters whose linear velocity and angular velocity are subject to some stochastic disturbances simultaneously. A switching control strategy for the original system is presented. The proposed controllers that guarantee the states of closed-loop system are asymptotically stabilized at the zero equilibrium point in probability.

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

ADAPTIVE SYNCHRONIZATION FOR A CLASS OF HIGH-DIMENSIONAL AUTONOMOUS UNCERTAIN CHAOTIC SYSTEMS

2007 ◽  
Vol 18 (03) ◽  
pp. 399-406 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Chaotic Systems ◽  
Identification Problem ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
High Dimensional ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Uncertain Chaotic Systems ◽  
Unknown System

This paper addresses the adaptive synchronization and parameters identification problem of a class of high-dimensional autonomous uncertain chaotic systems. It is proved that the controller and update rule can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the response system's unknown parameters. Chen system, coupled dynamos system and Rössler hyperchaotic system are used as examples for detailed description. The results of numerical simulations show the effectiveness of the adaptive controller.

TWO ADAPTIVE SYNCHRONIZATION METHODS OF UNCERTAIN CHEN SYSTEM

2009 ◽  
Vol 23 (26) ◽  
pp. 5163-5169 ◽  
Author(s):  
XINGYUAN WANG ◽  
MIN XU ◽  
HUAGUANG ZHANG
Keyword(s):  
Numerical Simulations ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Problem

This article addresses the adaptive synchronization problem of two Chen systems with uncertain parameters. Two adaptive synchronization methods are designed. In the two methods, we use only two controllers to synchronize uncertain Chen systems. It is theoretically proved that these two methods can make uncertain Chen systems asymptotically synchronized and identify the unknown parameters. Numerical simulations show the effectiveness of the proposed methods further. The comparisons of these two methods show: The method of theorem 1 is easier and more feasible than that of theorem 2, and the synchronization results are better.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

Sign in / Sign up

Export Citation Format

Share Document