scholarly journals Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Weiping Wang ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jialiang Yuan ◽  
Jinghua Xiao ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Real World ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Definition Of ◽  
First Time ◽  
Theoretical Results

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION CONTROL OF A LORENZ-LIKE SYSTEM

2008 ◽  
Vol 22 (15) ◽  
pp. 2453-2461 ◽  
Author(s):  
XINGYUAN WANG ◽  
YONG WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Uncertain System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Synchronization Control ◽  
System Parameters

This paper analyzes the synchronization control of new chaotic systems called Lorenz-like systems. Based on the Lyapunov stability theory, an adaptive controller and a parameter update rule are designed. It is proved that the controller and update rule not only achieve self-synchronization of Lorenz-like systems but can also make the Lorenz-like system asymptotically synchronized with the Rössler system, and further identify the uncertain system parameters. Numerical simulations have shown the effectiveness of the adaptive controller.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

scholarly journals Pinning synchronization of the drive and response dynamical networks with lag

2014 ◽  
Vol 24 (3) ◽  
pp. 257-270 ◽  
Author(s):  
Bohui Wen ◽  
Mo Zhao ◽  
Fanyu Meng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Schur Complement ◽  
Pinning Control ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
General Complex ◽  
Minimum Number

Abstract This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

scholarly journals Synchronization of Coupled Networks with Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Yi Zuo ◽  
Xinsong Yang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Nonlinear Perturbations ◽  
Coupled Networks ◽  
Barbalat Lemma ◽  
Asymptotic Synchronization ◽  
Theoretical Results

Asymptotic synchronization for a class of coupled networks with nondelayed and delayed couplings is investigated. A distinct feature of the network is that all the dynamical nodes are affected by uncertain nonlinear nonidentical perturbations. In order to synchronize the network onto a given isolate trajectory, a novel adaptive controller is designed to overcome the effects of the nonidentical uncertain nonlinear perturbations. The designed controller has better robustness than classical adaptive controller, since it can realize the synchronization goal whether the nodes have these perturbations or not. Based on the Lyapunov stability theory and the Barbalat lemma, sufficient conditions guaranteeing the asymptotic synchronization of the coupled network are derived. Two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results. Simulations also demonstrate that our adaptive controller has better robustness than existing ones.

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.

Nonlinear Control Law Design for Lateral Aircraft Dynamics at High Angles of Attack

2013 ◽  
Vol 325-326 ◽  
pp. 1210-1214
Author(s):  
Costin Ene
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Nonlinear Behavior ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Adaptive Backstepping ◽  
Type Design ◽  
Nonlinear Control Law ◽  
High Angles Of Attack

In this paper, an adaptive backstepping type design is proposed to control the complex nonlinear behavior of the wing rock phenomenon. This method, based on Lyapunov stability theory, can simultaneouslyachieve parameters identification and control.Finally numerical simulations are presented to justify the effectiveness of the proposed controller.

scholarly journals Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches

2017 ◽  
Vol 7 (3) ◽  
pp. 248-254
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

The main objective of this work is to discuss a generalized synchronization of a coupled chaotic identicaland nonidentical dynamical systems. We propose a method used to study generalized synchronization in masterslavesystems. This method, is based on the classical Lyapunov stability theory, utilizes the master continuous timechaotic system to monitor the synchronized motions. Various numerical simulations are performed to verify theeffectiveness of the proposed approach.

scholarly journals Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Wang ◽  
Yongguang Yu ◽  
Hu Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Convergence Speed ◽  
External Disturbances ◽  
Adaptive Controllers ◽  
Robust Synchronization ◽  
Hyperchaotic Systems

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

scholarly journals Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

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