Adaptive pinning control: A review of the fully decentralized strategy and its extensions

In this work, we review recent developments related to the problem of guiding a complex network of agents toward a synchronized state. Specifically, we focus on adaptive pinning control strategies, expounding those developed by the authors in the context of the existing literature, in which only a small fraction of the network nodes is directly controlled. The methodologies described herein are adaptive in the sense that the control and coupling gains are updated on the basis of the local mismatch with the desired trajectory and between coupled nodes, respectively. A selection of adaptive strategies recently proposed in the literature is reviewed, and the main stability results are expounded. As a numerical validation, the selected approaches are applied to control an ensemble of coupled mobile agents moving in a formation.