Adaptive Pinning Synchronization of Switching Networks with Arbitrary Topologies

We propose a novel design approach for pinning control of a dynamical network that achieves synchronization despite switching between arbitrary topologies. Unlike existing approaches, we consider weighted, directed, and even unconnected topologies as admissible connections that can be switched instantly. We present a selection algorithm that uses the current topology to identify a suitable set of nodes for control. Additionally, we consider a fixed pinning strategy to activate the required controllers to achieve synchronization, with their gains computed via adaptation laws based only on the neighbors of each pinned node. We derive sufficient conditions for the emergence of a stable synchronous state using common Lyapunov function theory and illustrate their efficacy through numerical simulations of networks that can switch instantaneously between arbitrary topologies.