CHAOS AND ROBUST ADAPTIVE SYNCHRONIZATION IN A NONLINEAR EMITTER–RECEIVER SYSTEM

2007 ◽  
Vol 17 (09) ◽  
pp. 3259-3274 ◽  
Author(s):  
F. M. MOUKAM KAKMENI ◽  
SAMUEL BOWONG
Keyword(s):  
Adaptive Observer ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Global Synchronization ◽  
Receiver System ◽  
Lipschitz Constants ◽  
Response Systems ◽  
Robust Adaptive ◽  
Synchronization Scheme

This work studies transitions to chaos and adaptive synchronization of a nonlinear emitter–receiver system in a drive–response framework. Safe bifurcations and explosive bifurcations are observed. A robust adaptive observer-based response system is designed to synchronize the emitter–receiver system with unknown parameters and external disturbances. Lyapunov stability ensures global synchronization between the drive and response systems even if Lipschitz constants on functions matrices and bound on uncertainties are unknown. Computer simulations are provided to illustrate the designed adaptive synchronization scheme.

ADAPTIVE OBSERVER BASED SYNCHRONIZATION OF A CLASS OF UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (08) ◽  
pp. 2425-2435 ◽  
Author(s):  
SAMUEL BOWONG ◽  
RENÉ YAMAPI
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Observer ◽  
Adaptive Synchronization ◽  
External Disturbances ◽  
Parameter Mismatch ◽  
Lipschitz Constants ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Robust Adaptive

This study addresses the adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. For a class of uncertain chaotic systems with parameter mismatch and external disturbances, a robust adaptive observer based on the response system is constructed to practically synchronize the uncertain drive chaotic system. Lyapunov stability theory ensures the practical synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of two illustrative examples are given to verify the effectiveness of the proposed method.

scholarly journals Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Meng ◽  
Xiaohong Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Small Region ◽  
Hopfield Neural Networks ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Lyapunov Stability Criterion ◽  
Order Extension

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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.

scholarly journals Novel Fuzzy-Modeling-Based Adaptive Synchronization of Nonlinear Dynamic Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shih-Yu Li ◽  
Chin-Sheng Chen ◽  
Lap-Mou Tam ◽  
Shun-Hung Tsai
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Adaptive Control Strategy ◽  
Modeling Strategy ◽  
Synchronization Scheme

In this paper, a novel fuzzy-model-based adaptive synchronization scheme and its fuzzy update laws of parameters are proposed to address the adaptive synchronization problem. The proposed fuzzy controller does not share the same premise of fuzzy system, and the numbers of fuzzy controllers is reduced effectively through the novel modeling strategy. In addition, based on the adaptive synchronization scheme, the error dynamic system can be guaranteed to be asymptotically stable and the true values of unknown parameters can be obtained. Two identical complicated dynamic systems, Mathieu-Van der pol system (M-V system) with uncertainties, are illustrated for numerical simulation example to show the effectiveness and feasibility of the proposed novel adaptive control strategy.

AN ADAPTIVE OBSERVER FOR CHAOS SYNCHRONIZATION OF A NONLINEAR ELECTRONIC CIRCUIT

2006 ◽  
Vol 16 (09) ◽  
pp. 2671-2679 ◽  
Author(s):  
HILAIRE FOTSIN ◽  
F. M. MOUKAM KAKMENI ◽  
SAMUEL BOWONG
Keyword(s):  
Chaos Synchronization ◽  
State Feedback ◽  
Electronic Circuit ◽  
Lyapunov Stability Theory ◽  
Coupled Systems ◽  
Adaptive Observer ◽  
Adaptive Synchronization ◽  
Electrical Circuits ◽  
Linear State ◽  
Synchronization Scheme

This Letter studies adaptive chaos synchronization between two coupled nonlinear electrical circuits using a linear state feedback. A simple and yet easily applicable algorithm is derived for adaptive chaos synchronization based on the Lyapunov stability theory. An adaptive linear state feedback is derived such that the coupled systems are globally synchronized. Numerical simulations show the effectiveness of the proposed synchronization scheme. A Pspice simulation of the adaptive synchronization process is performed to confirm the numerical results.

Robust Adaptive Controller Design for a Quadrotor Helicopter

2013 ◽  
Vol 284-287 ◽  
pp. 2296-2300 ◽  
Author(s):  
Kuang Shine Yang ◽  
Chi Cheng Cheng
Keyword(s):  
Attitude Control ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Sliding Mode ◽  
Underactuated System ◽  
Parameter Uncertainties ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Quadrotor Helicopter ◽  
Robust Adaptive

The quadrotor helicopter is designed to easily move in particular environments because it can take off and land in limited space and easily hover at a fixed location. For this reason, a robust adaptive sliding mode controller is developed to control of a quadrotor helicopter in the presence of external disturbances and parameter uncertainties. The quadrotor helicopter system is a typical underactuated system, which has fewer independent control actuators than degrees of freedom to be controlled. The main contribution here is to afford simulation and verification for the quadrotor helicopter flight controller under the assumption of unknown parameters. By utilizing the Lyapunov stability theorem, we can achieve asymptotic tracking of desired reference commands for the quadrotor helicopter, which is subject to both external disturbances and parametric uncertainties. From the simulation results, the controller was sufficient to achieve position and attitude control of the quadrotor helicopter system, which permits possible real time applications in the near future.

ADAPTIVE ROBUST SYNCHRONIZATION FOR A CLASS OF DIFFERENT UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 22 (23) ◽  
pp. 4069-4082 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Chaotic Systems ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Robust Controller ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Predicted Values

This paper addresses the adaptive synchronization problem of a class of different uncertain chaotic systems. A general adaptive robust controller and parameters update rule are designed. It is proved theoretically that the controller and update rule can make the drive-response systems with different structures asymptotically synchronized, and change the unknown parameters to constants when noise exists. When the drive system is certain, the unknown parameters of the response system can be updated to the predicted values. The results of numerical simulations show the effectiveness of the adaptive controller.

scholarly journals Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Zengyun Wang ◽  
Lihong Huang ◽  
Xuxin Yang ◽  
Dingyang Lu
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Adaptive Synchronization ◽  
Sliding Mode Controller ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Main Work ◽  
Robust Adaptive

This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

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