This paper investigates the pinning control strategy of BA scale-free network through numerical analysis. A new cost function is defined to measure the cost of pinning control. Compared with the control gain and the cost of pinning nodes with smallest degree or biggest degree, an interesting result is that a smaller control gain and a lower cost are achieved by using the control scheme of pinni...

This paper concerns pinning control in complex networks of dynamical systems, where an external forcing signal is applied to the network in order to align the state of all the systems to the forcing signal. By considering the control signal as the state of a virtual dynamical system, this problem can be studied as a synchronization problem. The main focus of this paper is to study how the effec...

Controlling complex networks is of paramount importance in science and engineering. Despite recent efforts to improve controllability and synchronous strength, little attention has been paid to the speed of pinning synchronizability (rate of convergence in pinning control) and the corresponding pinning node selection. To address this issue, we propose a hypothesis to restrict the control cost, ...

This chapter first introduces some complex network models and then gives both local and global stability conditions for complete synchronization of complex dynamical networks. In addition, the concept of virtual control of pinned complex dynamical networks is introduced to illustrate the principle of pinning control. The main reason is explained for why significantly less local controllers are ...

In this paper, pinning control in a system of moving agents (each one associated with a chaotic dynamical system) was investigated. In particular, we studied and compared two different strategies for pinning control and discussed the nontrivial relation between synchronization and chaotic agent control. Our results show how system parameters such as agent density are critical in order to reach ...

In this work we address the problem of controlling a complex network toward a synchronous evolution by using pinning control strategy. Considering this control approach, we investigate the effect of the number of pinned nodes and how the strategy performance behaves in accordance with the type of nodes that are chosen as the ones over which the control is applied. The roles of the control and c...

The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the co...