Synchronization control for discrete-time complex dynamical networks with dynamic links subsystem

In this paper, the synchronization of discrete-time complex dynamical network with dynamic links is investigated. From the angle of large-scale system, if the links and nodes are time-varying, the complex dynamical network may be regarded to be composed of nodes subsystem (NS) and links subsystem (LS). The weighted value of links between nodes can be regarded as the state variables of LS, the above two subsystems are mutually coupled. The two subsystems are modeled mathematically by the state difference equations, especially, the dynamics of LS is modeled as Riccati matrix difference equation without control input. Different from the previous researches, this work concerns simultaneously the dynamics of LS and NS, by which the synchronization of NS is investigated. Associated with the given dynamic reference target for LS, the nodes controller is synthesized to ensure the state synchronization of NS to be achieved with the assistance of the LS. Finally, the numerical simulation is given to illustrate the effectiveness of the proposed theoretical results in this paper.

Asymptotically tracking control for discrete time-varying link system to structural balance via determined external stimulations

This paper is concerned with the structural balance problem for complex dynamical network with the help of coupling effect related to the external stimulations. Consider a network with time-varying and value-weighted links, which can be regarded as a dynamic system. The link dynamic system is modeled as a Riccati matrix difference equation with the coupling matrix related to the external stimulations. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive a simple criterion for ensuring that the discrete link system asymptotically achieves structural balance, meanwhile, the external stimulations track a corresponding vector signal as well. Simulation examples are given to demonstrate the usefulness of the proposed control scheme in this paper.

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

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.

Robust exponential synchronization of a Markovian jump complex dynamical network with piecewise homogeneous Markovian parameters

This paper establishes a stochastic synchronization method for a Markovian jump complex dynamical network (MJCDN) with time-delay and uncertainties. The considered Markovian structure is piecewise-homogeneous with piecewise-constant time-varying transition rates (TRs). Two Markovian signals are utilized to construct the piecewise-homogeneous Markovian structure. A low-level Markovian signal with time-varying TRs governs the switching between the system dynamics while it is managed by a high-level Markovian signal. Due to the effect of imperfections induced by modeling errors in the system dynamics, some parametric norm-bounded uncertainties are considered. In addition, uncertain TR matrix is considered which means that inaccurate or uncertain information for each element of the TR matrix is allowable. This modelling makes the MJCDN to be more general and applicable than the existing ones. Synchronization conditions are obtained and reported in the form of linear matrix inequalities by the help of Lyapunov–Krasovskii theory, Wirtinger-based integral inequality approach and reciprocally convex technique. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Structural balance for discrete-time complex dynamical network associated with the controlled nodes

In this paper, the discrete-time complex dynamical networks with dynamic weighted value of connection relationships are regarded to be composed of the node and link subsystems, and the state variables of the two subsystems are mutually coupled. Different from most of the existing researches on synchronization or stabilization of nodes, the emphasis of this paper is on the links instead of nodes. This paper mainly focuses on the generation mechanism of structural balance in the link subsystem, the nodes only play an auxiliary role. Associated with the dynamic coupling term in the link subsystem, the suitable controller is proposed for node subsystem such that the structural balance of link subsystem without control input be achieved indirectly. Finally, a numerical simulation is given to show the effectiveness of the method in this paper.

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

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.