scholarly journals Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Control Cost ◽  
Synchronization Problem ◽  
Delayed Coupling ◽  
Control Scheme ◽  
Successful Control ◽  
Synchronization Pattern

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

scholarly journals Cluster Synchronization of Stochastic Complex Networks with Markovian Switching and Time-Varying Delay via Impulsive Pinning Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xuan Zhou ◽  
Kui Luo
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Markovian Switching ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
Stochastic Complex Networks

This paper studies the cluster synchronization of a kind of complex networks by means of impulsive pinning control scheme. These networks are subject to stochastic noise perturbations and Markovian switching, as well as internal and outer time-varying delays. Using the Lyapunov-Krasovskii functional, Itö’s formula, and some linear matrix inequalities (LMI), several novel sufficient conditions are obtained to guarantee the desired cluster synchronization. At the end of this writing, a numerical simulation is given to demonstrate the effectiveness of those theoretical results.

scholarly journals Pinning Cluster Synchronization in Linear Hybrid Coupled Delayed Dynamical Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Anping Bao ◽  
Ting Wang ◽  
Shumin Fei ◽  
Xiaomin Tian
Keyword(s):  
Control Strategy ◽  
Kronecker Product ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dynamical Networks ◽  
Delayed Dynamical Networks

The problem on cluster synchronization will be investigated for a class of delayed dynamical networks based on pinning control strategy. Through utilizing the combined convex technique and Kronecker product, two sufficient conditions can be derived to ensure the desired synchronization when the designed feedback controller is employed to each cluster. Moreover, the inner coupling matrices are unnecessarily restricted to be diagonal and the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which greatly improve the present methods. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism.

scholarly journals Impulsive Pinning Markovian Switching Stochastic Complex Networks with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chen Xu ◽  
Jingyi Wang ◽  
Jianwen Feng ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Functional Method ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Stochastic Complex Networks

The synchronization problem of stochastic complex networks with Markovian switching and time-varying delays is investigated by using impulsive pinning control scheme. The complex network possesses noise perturbations, Markovian switching, and internal and outer time-varying delays. Sufficient conditions for synchronization are obtained by employing the Lyapunov-Krasovskii functional method, Itö's formula, and the linear matrix inequality (LMI). Numerical examples are also given to demonstrate the validity of the theoretical results.

Vibration control of network-based offshore structures subject to earthquakes

2021 ◽  
pp. 014233122110259
Author(s):  
Hua-Nv Feng ◽  
Bao-Lin Zhang ◽  
Yan-Dong Zhao ◽  
Hui Ma ◽  
Hao Su ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Offshore Structures ◽  
Delay Systems ◽  
Linear Matrix ◽  
Seismic Responses ◽  
Marine Structures ◽  
Damping Control ◽  
Marine Structure ◽  
Uncertain Model ◽  
Control Scheme

Marine structures are inevitably influenced by parametric perturbations as well as multiple external loadings. Among these loadings, earthquake is generally more destructive and unpredictable than others. It is significant to develop effective active control schemes to guarantee the safety, stability, and integrity of marine structures subject to earthquakes and parametric perturbations. In this paper, the problem of networked [Formula: see text] robust damping control is addressed to stabilize a marine structure subject to earthquakes. First, in consideration of perturbations of the structure parameters, an uncertain model of the networked marine structure under earthquakes is presented. Second, a robust networked [Formula: see text] control scheme is presented to suppress seismic responses of the structure. By using stability theory of time-delay systems, several sufficient conditions on robust stability of the networked marine structure system are obtained, and the linear matrix inequality methods are utilized to solve the gain matrix of the controller. Finally, simulation indicates that compared with the traditional robust [Formula: see text] control and the proposed networked [Formula: see text] control, the seismic responses amplitudes of the marine structure under the two controllers are almost the same, while the latter is more economic than the former.

scholarly journals Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

2021 ◽  
Author(s):  
Chao Ma ◽  
Liziyi Hao ◽  
Hang Fu
Keyword(s):  
Neural Network ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Markov Jump ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
The Neural Network ◽  
Takagi Sugeno

AbstractThis paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

The Control of a Neural Complex Network

2014 ◽  
Vol 687-691 ◽  
pp. 444-446
Author(s):  
Fan Di Zhang
Keyword(s):  
Neural Network ◽  
Community Structure ◽  
Lyapunov Stability ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Cluster Synchronization ◽  
Special Cases

In this paper, the synchronization of a neural network with community structure is investigated. Cluster projective generalizes previously existing synchronization schemes. The cluster projective synchronization is more general that includes projective synchronization and cluster synchronization, as its special cases. The cluster projective synchronization of these networks is discussed via some pinning control strategy. Several sufficient conditions for the network to achieve cluster projective synchronization are derived based on Lyapunov stability theory. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

Delayed Output Feedback Control for Nonlinear Systems With Fuzzy Observers

2012 ◽  
Author(s):  
Mansour Karkoub ◽  
Tzu Sung Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Scheme

In this paper, the design problem of delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno type fuzzy linear model with an on-line update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The linguistic information is developped by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. The filtered tracking error dynamics are designed to satisfy the Strictly Positive Realness (SPR) condition. Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs), some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and consequently an H∞ tracking control is achieved. Finally, a numerical example of a two-link robot manipulator is given to illustrate the effectiveness of the proposed control scheme.

Reliable Robust Control Design for Uncertain Mechanical Systems

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
R. Sakthivel ◽  
Srimanta Santra ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Linear Matrix ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Stiffness Matrices ◽  
Control Scheme ◽  
Robust Control Design ◽  
Varying Delay

In this article, we consider the problem of reliable H∞ control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H∞ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H∞ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H∞ performance index over some existing works.

scholarly journals Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Fang ◽  
Kang Yan ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Impulsive Synchronization ◽  
Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

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