Kybernetika 54 no. 1, 30-40, 2018

Adaptive tracking via pinning in networks of nonidentical nodes

Juan Gonzalo Barajas-RamírezDOI: 10.14736/kyb-2018-1-0030


We investigate the control of dynamical networks for the case of nodes, that although different, can be make passive by feedback. The so-called V-stability characterization allows for a simple set of stabilization conditions even in the case of nonidentical nodes. This is due to the fact that under V-stability characterization the dynamical difference between node of a network reduces to their different passivity degrees, that is, a measure of the required feedback gain necessary to make the node stable at a desired solution. We propose a pinning control strategy that extends this approach to solve the tracking problem, furthermore using an adaptive controller approach we provide a methodology to impose a common reference trajectory to a network of different nodes by pinning only a few of them to the desired solution. We illustrate our results with numerical simulation of well-known benchmark systems.


adaptive control, pinning control, complex networks, tracking problem


05C82, 34H05, 49K15


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