Exponential synchronization in complex-variable network with distributed delays via intermittent control

2017 ◽  
Vol 28 (07) ◽  
pp. 1750089 ◽  
Author(s):  
Sulan He ◽  
Guisheng Yi ◽  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Exponential Synchronization ◽  
Distributed Delays ◽  
Intermittent Control ◽  
Control Gain ◽  
Analysis Technique ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
And Control ◽  
Theoretical Results

In this paper, exponential synchronization in complex-variable network with distributed delays is investigated. By utilizing intermittent control scheme, some effective controllers are designed. Based on the Lyapunov function method and mathematical analysis technique, some synchronization criteria with respect to the system parameters, control gain and control rate are presented. From the criteria, for any given dynamical network, the needed values of control gains and rate can be easily estimated. Finally, two numerical simulations are performed to verify the derived theoretical results.

Adaptive intermittent control for exponential synchronization of directed networks with complex-variable systems and distributed delays coupling

2018 ◽  
Vol 29 (11) ◽  
pp. 1850110 ◽  
Author(s):  
Shuiming Cai ◽  
Xiaojing Li ◽  
Feilong Zhou
Keyword(s):  
Complex Variable ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Distributed Delays ◽  
Control Technique ◽  
Intermittent Control ◽  
Directed Networks ◽  
Control Gain ◽  
Intermittent Feedback

In this paper, adaptive exponential synchronization of directed networks with complex-variable systems and distributed delays coupling is investigated. An adaptive nonperiodical intermittent control scheme is adopted to realize exponential synchronization of such complex-variable directed dynamical networks. Based on the complex inequality, piecewise analysis method and Lyapunov stability theory, some sufficient conditions guaranteeing globally exponential synchronization are established. Different from previous works, here the designed adaptive update law for intermittent feedback control gain does not explicitly depend on time, which makes the adaptive nonperiodical intermittent control technique more convenient to implement in realistic applications. Moreover, it is indicated that the established synchronization criteria depend on the control rates rather than the control periods or control widths, and therefore the control periods can be optionally chosen for practical problems. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results.

scholarly journals Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

2021 ◽  
Vol 26 (6) ◽  
pp. 993-1011
Author(s):  
Mei Liu ◽  
Jie Chen ◽  
Haijun Jiang ◽  
Zhiyong Yu ◽  
Cheng Hu ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Auxiliary Function ◽  
Intermittent Control ◽  
Global Synchronization ◽  
Delayed Systems ◽  
Control Gain ◽  
Analysis Technique ◽  
Theoretical Results

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.

Adaptive impulsive cluster synchronization in community network with nonidentical nodes

2016 ◽  
Vol 27 (01) ◽  
pp. 1650010 ◽  
Author(s):  
Xiaoli Gong ◽  
Luyining Gan ◽  
Zhaoyan Wu
Keyword(s):  
Impulsive Control ◽  
Adaptive Strategy ◽  
Cluster Synchronization ◽  
Community Network ◽  
Analysis Technique ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
Nonidentical Nodes ◽  
Proper Values ◽  
Theoretical Results

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. Through introducing proper adaptive strategy into impulsive control scheme, adaptive impulsive controllers are designed for achieving the cluster synchronization. In this adaptive impulsive control scheme, for any given networks, the impulsive gains can adjust themselves to proper values according to the proposed adaptive strategy when the impulsive intervals are fixed. The impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains are fixed. Both community networks without and with coupling delay are considered. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria are derived. Several numerical examples are performed to verify the effectiveness of the derived theoretical results.

scholarly journals Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality

2022 ◽  
Vol 7 (3) ◽  
pp. 4711-4734
Author(s):  
Xingxing Song ◽  
◽  
Pengfei Zhi ◽  
Wanlu Zhu ◽  
Hui Wang ◽  
...  
Keyword(s):  
Exponential Synchronization ◽  
Synchronization Control ◽  
Intermittent Control ◽  
Parameter Mismatch ◽  
Synchronization Problem ◽  
Control Gain ◽  
Control Scheme ◽  
Vector Information ◽  
Memristive Neural Network ◽  
The Stability

<abstract><p>In this paper, we study the exponential synchronization problem of a class of delayed memristive neural networks(MNNs). Firstly, a intermittent control scheme is designed to solve the parameter mismatch problem of MNNs. A discontinuous controller with two tunable scalars is designed, and the upper limit of control gain can be adjusted flexibly. Secondly, an augmented Lyaponov-Krasovskii functional(LKF) is proposed, and vector information of N-order canonical Bessel-Legendre(B-L) inequalities is introduced. LKF method is used to obtain the stability criterion to ensure exponential synchronization of the system. The conservatism of the result decreases with the increase of the order of the B-L inequality. Finally, the effectiveness of the main results is verified by two simulation examples.</p></abstract>

scholarly journals Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Lihong Yan ◽  
Junmin Li
Keyword(s):  
Adaptive Learning ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Time Varying ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Synchronization Problem ◽  
Coupling Strengths ◽  
Inequality Techniques ◽  
Theoretical Results

In this paper, exponential synchronization problem of complex dynamical networks with unknown periodically coupling strengths was investigated. An aperiodically intermittent control synchronization strategy is proposed. Based on Lyapunov exponential stability theory, inequality techniques, and adaptive learning laws design, some sufficient exponential synchronization criteria for complex dynamical network with unknown periodical coupling weights are obtained. The numerical simulation example is presented to illustrate the feasibility of theoretical results.

Design and control of a two-dimensional telerobotic system with a haptic interface

2003 ◽  
Vol 217 (3) ◽  
pp. 169-185
Author(s):  
M-G Her ◽  
M Karkoub ◽  
K-S Hsu
Keyword(s):  
Haptic Interface ◽  
Two Dimensional ◽  
Direct Drive ◽  
Closed Loop System ◽  
Human Arm ◽  
Control Scheme ◽  
Reaction Forces ◽  
And Control ◽  
Theoretical Results ◽  
Good Agreement

A model for a ‘master-slave’ two-dimensional telerobotic dynamic system with a haptic interface device is derived. The telerobotic system consists of a ‘master’ robot, which is a direct-drive robot operated by a human arm, and a ‘slave’ robot, which is an x-y type pallet located at a remote site. When the active handle of the master is moved along an arbitrary trajectory, the remote slave duplicates the motion in a constrained or unconstrained environment. The behaviour of the environment is felt by the operator through the active handle of the master. This is achieved by feeding back the disturbance and reaction forces from the environment and the loads to the active handle. Consequently, the operator gets a feel of the task being performed without being physically at the location of the task. A control scheme is devised for the telerobotic system to establish smooth communication between the master and slave robots. This control scheme integrates the dynamics of the human arm, actuators and the environment in the closed-loop system. It was shown that the experimental and the theoretical results are in good agreement and that the design controller is robust to constrained/unconstrained environments.

scholarly journals Structure Identification of Fractional-order Complex-variable Network With Complex Coupling

2021 ◽  
Author(s):  
Mingcong Zhou ◽  
Zhaoyan Wu
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Topological Structure ◽  
Dynamical Behavior ◽  
Critical Issue ◽  
Structure Identification ◽  
Order Complex ◽  
System Parameters ◽  
Lyapunov Function Method ◽  
Theoretical Results

Abstract Fractional-order complex-variable dynamical network with complex coupling is considered in this paper. The topological structures and system parameters are assumed to be unknown. As we know, the topological structure and system parameters play a key role on the dynamical behavior of complex network. Thus, how to effectively identify them is a critical issue for better studying the network. Through designing proper controllers and updating laws, two corresponding network estimators are constructed. Based on the Lyapunov function method and Gronwall-Bellman integral inequality, the results are analytically derived. Finally, two numerical examples are performed to illustrate the feasibility of the theoretical results.

scholarly journals Pinning Adaptive Synchronization of Delayed Coupled Dynamical Networks via Periodically Intermittent Control

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xueliang Liu ◽  
Shengbing Xu
Keyword(s):  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Theoretical Results

This paper investigates the exponential synchronization problem of delayed coupled dynamical networks by using adaptive pinning periodically intermittent control. Based on the Lyapunov method, by designing adaptive feedback controller, some sufficient conditions are presented to ensure the exponential synchronization of coupled dynamical networks with delayed coupling. Furthermore, a numerical example is given to demonstrate the validity of the theoretical results.

SYNCHRONIZATION OF COMPLEX-VARIABLE DYNAMICAL NETWORKS WITH COMPLEX COUPLING

2013 ◽  
Vol 24 (02) ◽  
pp. 1350007 ◽  
Author(s):  
ZHAOYAN WU ◽  
XINCHU FU
Keyword(s):  
Complex Variable ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control Scheme ◽  
General Network ◽  
Adaptive Coupling ◽  
Theoretical Results

In this paper, synchronization of complex-variable dynamical networks with complex coupling is investigated. An adaptive feedback control scheme is adopted to design controllers for achieving synchronization of a general network with both complex inner and outer couplings. For a network with only complex inner or outer coupling, pinning control and adaptive coupling strength methods are adopted to achieve synchronization under some assumptions. Several synchronization criteria are derived based on Lyapunov stability theory. Numerical simulations are provided to verify the effectiveness of the theoretical results.

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