Node-to-node pinning control of complex networks

Abstract

In this paper, we study pinning controllability of oscillator networks. We present necessary conditions for network pinning controllability based on the spectral properties of the oscillator network and the individual oscillator dynamics. We define a performance metric for pinning-control systems based on the location of pinned sites, the pinning-control gains, and the network topology. We show that for any network structure, uniform pinning of all the network nodes maximizes the pinning-control performance. We propose the node-to-node pinning-control strategy to optimize the control performance while avoiding to simultaneously control all the network sites. In this novel strategy, the pinning-control action rapidly switches from one node to another with the goal of taming the oscillator network dynamics to the desired trajectory. We illustrate our findings through numerical simulations on networks of Rossler oscillators.

Drive network to a desired orbit by pinning control

“…Distinctly, it turns out that the developed control tactics consider both the different influences and contributions of all nodes in synchronization seeking processes. In general, among most previous studies, the controlled synchronization state is only taken into account to be a special solution of the homogenous systems, that is, s(t) = f (s(t)) [1,4,5,8,10,18,19,20,22,23,24,27,29,31,30,34,35,33,32,36,38,39,40,41]. Or consider an average of all the nodes states in the networks, namely, [9,37].…”

“…And later on, Yu et al [36] concerned with pinning performance of complex dynamical network. Other research works about pinning control of complex networks can be seen in [8,12,17,22,23,24,26,30,31,32,33,34,35,40,41] and many references cited therein.…”

“…To reduce the number of controlled nodes, some feedback injections have been added to a fraction of network nodes, which is known as pinning control. As a result, some researchers have focused on the investigations different pinning control strategies for various complex dynamical networks [5,8,10,14,22,23,24,25,26,29,30,31,32,33,34,35,36,39]. For example, Wang and Chen [29] revealed that, it is much more effective to pin some most-highly connected nodes than to pin randomly selected nodes since the extremely inhomogeneous connectivity distribution of scale-free networks.…”

Adaptive node-to-node pinning synchronization control of complex networks

“…18 and 19 where sufficient and necessary conditions for the stability of synchronization of the desired common solution were also given. The problem of selecting the type of nodes that should be pinned in order to improve synchronization performance 20 by minimizing synchronization time, and driving the system to a desired state is still an open problem; however, it has been proposed by Porfiri et al 21 a node-to-node pinning strategy to maximize synchronization performance, i.e., minimize synchronization time. In node-to-node pinning control, just one node is pinned, and at each instant of time multiple of the switching period T, a new node is randomly chosen to be pinned.…”

Event-Triggered Pinning Control of Switching Networks

“…Topology variations are due to imperfect communication between agents, or simply the existence of a proximity range beyond which communication is not possible. A large number of papers investigate synchronization [15]- [18] or pinning control [19]- [21] under time-varying interaction topologies. Note that communication failures can usually be regarded as switching events.…”