Decentralized stabilization for structurally balanced networks with similar nodes

2019 ◽  
Vol 33 (12) ◽  
pp. 1950146
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Lili Zhang ◽  
Jiang Xiong ◽  
Wenli Wang
Keyword(s):  
Information Flow ◽  
Complex Dynamical Networks ◽  
Communication Delays ◽  
Stabilization Problem ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Decentralized Stabilization ◽  
Delayed Information ◽  
Decentralized Controllers ◽  
Balanced Networks

This paper studies the stabilization problem of complex dynamical networks with nonlinear similar nodes and arbitrary finite communication delays, while the networks are structural balance. For the considered networks, the information flow is undirected or directed, and only locally delayed information can be used for each node. We derive that stabilization of structurally balanced networks can be realized by designing decentralized controllers, when the associated assumptions are true. Furthermore, the proposed stabilization schemes are also useful to the structurally balanced networks without communication delays. Finally, the simulations are presented to show the effectiveness of the method in this paper.

scholarly journals Structural Balance Control of Complex Dynamical Networks Based on State Observer for Dynamic Connection Relationships

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Jiang Xiong ◽  
Yong Pan ◽  
Yuanyuan Huang
Keyword(s):  
Balance Control ◽  
Lyapunov Stability Theory ◽  
State Observer ◽  
The State ◽  
Complex Dynamical Networks ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Practical Applications ◽  
Coupled Subsystems

This paper investigates the observer-based structural balance control for a class of complex dynamical networks. Generally speaking, a complete complex dynamical network is composed of two coupled subsystems, which are called node subsystem (NS) and connection relationship subsystem (CS), respectively. Similar to synchronization and stabilization of networks, the structural balance is another phenomenon of networks and determined by the state of connection relationships. However, it is not feasible to design the controller for the CS directly because the states of the connection relationships are difficult to be measured accurately in practical applications. In order to solve this problem, a state observer for the CS has been designed. Thus, the structural balance controller in the CS can be directly designed by using the estimation information of the state observer. Then, with the help of the Lyapunov stability theory, it is proved that the CS can asymptotically track a given structural balance matrix under the influence of the observer-based controller. Finally, the results derived from this paper are demonstrated by performing a numerical example.

scholarly journals Control of Synchronization and Stability for Nonlinear Complex Dynamical Networks with Different Dimensional Similar Nodes and Coupling Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Luo Yi-ping ◽  
Luo Xin ◽  
Deng Fei ◽  
Hu Jun-qiang
Keyword(s):  
Complex Dynamical Networks ◽  
Time Varying ◽  
Lyapunov Stability Theorem ◽  
Dynamical Networks ◽  
Time Varying Delay ◽  
Decentralized Controllers ◽  
Coupling Time ◽  
The Stability ◽  
Definition Of ◽  
Varying Delay

This paper discusses the stability and synchronization for the nonlinear coupled complex networks with different dimensional nodes, and the external coupling satisfies the condition of dissipation. The definition of synchronization of the complex dynamical networks is proposed as the manifold. By Lyapunov stability theorem, the decentralized controllers with similar parameters are designed to synchronize such dynamical networks asymptotically in which the characteristics are variable delayed. Finally, a numerical example is given to illustrate the effectiveness of the designed method.

Adaptive control for complex dynamical networks with structural balance via external stimulus signals

2019 ◽  
Vol 33 (33) ◽  
pp. 1950415
Author(s):  
Yi Peng ◽  
Yinhe Wang ◽  
Zilin Gao ◽  
Lili Zhang
Keyword(s):  
Adaptive Control ◽  
Balance Control ◽  
External Stimulus ◽  
Complex Dynamical Networks ◽  
Dynamical Characteristic ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Dynamical Network ◽  
Matrix Differential

This paper investigates the adaptive structural balance control of complex dynamical networks by employing the controlled external stimulus signals which are coupled and transmitted to the dynamics of complex dynamical network. The control objective is to assure the asymptotical convergence of the dynamical links to the structural balance by the controlled external stimulus signals. The dynamical links of complex dynamical network are represented in this paper mathematically as the Riccati matrix differential equation with the controlled external stimulus signals which are coupled approximately in the form of Hebb rule. Compared with the existing results which are mainly concerned with the dynamical characteristics of nodes such as synchronization, this paper is mainly focused on the dynamical characteristic of links so named as the structural balance which is asymptotically obtained by the adaptive control scheme of external stimulus signals. Finally, a simulation example is given to show the validity of result proposed in this paper.

Adaptive Control of the Structural Balance for a Class of Complex Dynamical Networks

2020 ◽  
Vol 33 (3) ◽  
pp. 725-742
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Yi Peng ◽  
Lizhi Liu ◽  
Haoguang Chen
Keyword(s):  
Adaptive Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Structural Balance

Adaptive control of structural balance for complex dynamical networks based on dynamic coupling of nodes

2018 ◽  
Vol 32 (04) ◽  
pp. 1850042 ◽  
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Lili Zhang
Keyword(s):  
Large Scale ◽  
The State ◽  
Point Of View ◽  
Complex Dynamical Networks ◽  
Relationship Matrix ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Practical Applications ◽  
System A ◽  
The Social

In the existing research results of the complex dynamical networks controlled, the controllers are mainly used to guarantee the synchronization or stabilization of the nodes’ state, and the terms coupled with connection relationships may affect the behaviors of nodes, this obviously ignores the dynamic common behavior of the connection relationships between the nodes. In fact, from the point of view of large-scale system, a complex dynamical network can be regarded to be composed of two time-varying dynamic subsystems, which can be called the nodes subsystem and the connection relationships subsystem, respectively. Similar to the synchronization or stabilization of the nodes subsystem, some characteristic phenomena can be also emerged in the connection relationships subsystem. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. This paper focuses on the structural balance in dynamic complex networks. Generally speaking, the state of the connection relationships subsystem is difficult to be measured accurately in practical applications, and thus it is not easy to implant the controller directly into the connection relationships subsystem. It is noted that the nodes subsystem and the relationships subsystem are mutually coupled, which implies that the state of the connection relationships subsystem can be affected by the controllable state of nodes subsystem. Inspired by this observation, by using the structural balance theory of triad, the controller with the parameter adaptive law is proposed for the nodes subsystem in this paper, which may ensure the connection relationship matrix to approximate a given structural balance matrix in the sense of the uniformly ultimately bounded (UUB). That is, the structural balance may be obtained by employing the controlling state of the nodes subsystem. Finally, the simulations are used to show the validity of the method in this paper.

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