On pinning control of some typical discrete-time dynamical networks

Criteria for stochastic pinning control of networks of chaotic maps

“…20,29 While considerable efforts have been devoted to continuous-time dynamical systems, the analysis of discrete maps is a relatively untapped research area with our ability to effectively control the evolution of such systems being currently limited to few scenarios. [31][32][33] For example, in Ref. 31, the authors generalize the classical master stability function introduced in Ref.…”

“…As demonstrated through extensive simulations in Ref. 33, pinning control of discrete-time dynamical networks is a challenging task, whereby direct control of a large fraction of the network nodes is generally required.…”

“…With respect to animal grouping, such a desired trajectory may be represented by leaders, who seek to guide their conspecifics towards set locations. 16 So-called pinning control techniques [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] have been recently introduced to efficiently address this control problem. Within these schemes, an external node, referred to as the pinner, generates a reference trajectory, which is used to exert a control action only on a small fraction of the network nodes, termed the pinning sites.…”

Pinning synchronization for a class of chaotic complex networks with H∞performance

“…It's often impossible to add controllers to all nodes. Then, a literal solution is to control only a small fraction of nodes, which is known as pinning control [6][7][8][9][10][11][12][13][14]20] . Obviously, pinning control is more suitable to be applied in a large-scale network, as it can reduce the numbers of the controlled nodes and control costs in practical engineering applications.…”

Machine learning via dynamical processes on complex networks

“…Some works concerning the use of transversal Lyapunov exponents to prove synchronization (Li and Chen, 2003) or control (Li and Wang, 2004) of coupled chaotic maps can be found in the literature. However, the parameter's constraints to achieve an asymptotical stable behavior have showed to be too strong for discrete-time systems, hampering the pin control task (Zhang et al, 2010). On the other hand, for the linear system proposed in this work, we are able to establish some specific conditions on the parameter's values in order to guarantee the desired asymptotic behavior.…”