Generalized Synchronization of Chaos in RCL-Shunted Josephson Junction with Uncertain Parameters

2012 ◽  
Vol 157-158 ◽  
pp. 752-756
Author(s):  
Na Fang ◽  
Jie Fang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Josephson Junction ◽  
Stability Theory ◽  
Chaotic Dynamics ◽  
Control Method ◽  
Uncertain Parameters ◽  
Generalized Synchronization ◽  
Nonlinear Feedback ◽  
Scaling Factors

This paper investigates the generalized synchronization of chaotic dynamics in resistive capacitive inductance (RCL)-shunted Josephson junctions with uncertain parameters.Based on Lyapunove stability theory and adaptive control method, unified nonlinear feedback controller and the parameter update laws are pesented .Numerical simulation illustrate that the system can realize generalized synchronization by different scaling factors .

A Modification of Pragmatical Generalized Synchronization of Chaotic Systems with Uncertain Parameters by Adaptive Control

2012 ◽  
Vol 442 ◽  
pp. 375-378 ◽  
Author(s):  
Wen Guang Zhang ◽  
Jun Wei Lei ◽  
Guo Qiang Liang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Chaotic Systems ◽  
Uncertain Parameters ◽  
Generalized Synchronization ◽  
Kutta Method ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Runge Kutta Method

A modification to the synchronization law in [Zheng-Ming Ge, Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control, Physica D (2007) 87-94] is proposed. To verify and demonstrate the effectiveness of the proposed method, a numerical simulation is done and the fourth-order Runge-Kutta method is used to solve the system with time step size 0.001.

scholarly journals Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shih-Yu Li ◽  
Cheng-Hsiung Yang ◽  
Li-Wei Ko ◽  
Chin-Teng Lin ◽  
Zheng-Ming Ge
Keyword(s):  
Adaptive Control ◽  
Stability Theory ◽  
Initial Conditions ◽  
Stability Theorem ◽  
Phase Portraits ◽  
Adaptive Synchronization ◽  
Complex Signal ◽  
Uncertain Parameters ◽  
Chaotic Motions ◽  
Lorentz System

We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the similar chaotic signal of time-reversed Lorentz system. In addition, pragmatical asymptotically stability theorem and an assumption of equal probability for ergodic initial conditions (Ge et al., 1999, Ge and Yu, 2000, and Matsushima, 1972) are proposed to strictly prove that adaptive control can be accomplished successfully. The current scheme of adaptive control—by traditional Lyapunov stability theorem and Barbalat lemma, which are used to prove the error vector—approaches zero, as time approaches infinity. However, the core question—why the estimated or given parameters also approach to the uncertain parameters—remains without answer. By the new stability theory, those estimated parameters can be proved approaching the uncertain values strictly, and the simulation results are shown in this paper.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

A Model Reference Adaptive Control of a Magnetorheological Fluid Brake

2012 ◽  
Vol 77 ◽  
pp. 96-102
Author(s):  
Riccardo Russo ◽  
Mario Terzo
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Tracking Error ◽  
Magnetorheological Fluid ◽  
Model Reference Adaptive Control ◽  
Uncertain Parameters ◽  
Model Reference ◽  
Braking Torque ◽  
Feedback Control Method ◽  
Model Reference Adaptive

The paper describes an experimental/theoretical activity that involves a magnetorheological fluid brake (MRFB). The variability affecting the plant parameters suggests the employment of a model reference adaptive control finalized to regulate the braking torque. This feedback control method is able to minimize the tracking error in presence of a plant characterized by a known dynamics and uncertain parameters. Numerical simulations have been carried out and the obtained results confirm the goodness of the proposed approach.

Sign in / Sign up

Export Citation Format

Share Document