On the Pinning Synchronization of Switching Networks

Resumen: We investigate the pinning synchronization problem for networks that arbitrarily switch between a set of admissible connection topologies. We consider that both connections and controller gains can arbitrarily switch, then we investigate three scenarios to achieve network synchronization. In the first case, both topology and controller arbitrarily change at different times. In the second case, both switch at the same time. While in the third, the controller remains fixed for all time. In all scenarios, the controller is applied only to the node with the largest node degree of each admissible topology. Then, we can easily compare the control requirements of the different scenarios. We find that a fixed controller requires a smaller control gain than an arbitrary switching gain. However, if both topology and gains commute at the same time, it is possible to use even smaller control gains since one can use the minimum for each admissible topology. We illustrate our results with numerical simulation of switching networks of Lorenz systems.

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Juan Gonzalo Barajas-Ramirez & Isaac Leonel López-García. On the Pinning Synchronization of Switching Networks. Memorias del Congreso Nacional de Control Automático, pp. 1-5, 2020.

Palabras clave

Pinning control, Synchronization, Dynamical networks, Switching dynamics

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