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.

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 A New Model for Complex Dynamical Networks Considering Random Data Loss

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 797
Author(s):  
Xu Wu ◽  
Guo-Ping Jiang ◽  
Xinwei Wang
Keyword(s):  
Network Model ◽  
Network Models ◽  
Lyapunov Stability Theory ◽  
Complex Dynamical Networks ◽  
Output Coupling ◽  
Data Loss ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
Proposed Model

Model construction is a very fundamental and important issue in the field of complex dynamical networks. With the state-coupling complex dynamical network model proposed, many kinds of complex dynamical network models were introduced by considering various practical situations. In this paper, aiming at the data loss which may take place in the communication between any pair of directly connected nodes in a complex dynamical network, we propose a new discrete-time complex dynamical network model by constructing an auxiliary observer and choosing the observer states to compensate for the lost states in the coupling term. By employing Lyapunov stability theory and stochastic analysis, a sufficient condition is derived to guarantee the compensation values finally equal to the lost values, namely, the influence of data loss is finally eliminated in the proposed model. Moreover, we generalize the modeling method to output-coupling complex dynamical networks. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed model.

EFFECTS OF COUPLING DELAYS ON SYNCHRONIZATION IN LUR'E COMPLEX DYNAMICAL NETWORKS

2010 ◽  
Vol 20 (11) ◽  
pp. 3565-3584 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Complex Dynamical Networks ◽  
Lyapunov Functionals ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Decomposition Approach ◽  
Lur’E System ◽  
Numerical Example ◽  
Dynamical Network ◽  
Delay Decomposition Approach ◽  
Delay Decomposition

This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.

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

Synchronization of uncertain complex dynamical networks via adaptive control

2009 ◽  
Vol 19 (5) ◽  
pp. 495-511 ◽  
Author(s):  
Lei Wang ◽  
Huaping Dai ◽  
Xiangjie Kong ◽  
Youxian Sun
Keyword(s):  
Adaptive Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks

Topological Identification of Complex Dynamical Network with Communities and Node Delay

2013 ◽  
Vol 411-414 ◽  
pp. 2093-2097
Author(s):  
Jiang Ang Zhang ◽  
Yan Dong Chu ◽  
Wen Ju Du
Keyword(s):  
Parameter Identification ◽  
Hierarchical Structure ◽  
Invariance Principle ◽  
Topological Structure ◽  
Complex Dynamical Networks ◽  
Complex Dynamical Network ◽  
Network Systems ◽  
Dynamical Network ◽  
General Complex ◽  
Real Complex

Recently, various papers investigated the topology identification and parameter identification of uncertain general complex dynamical networks. However, in many real complex dynamical network systems, there exists community or hierarchical structure and node delay. Based on LaSalle’s invariance principle, in this letter, an adaptive controlling method is proposed to identify unknown topological structure for general weighted complex dynamical network with community and node delay. Illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme.

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