  Synchronization is a widespread phenomenon observed across natural and
artificial networked systems. It often manifests itself by clusters of units
exhibiting coincident dynamics. These clusters are a direct consequence of the
organization of the Laplacian matrix eigenvalues into spectral localized
blocks. We show how the concept of spectral blocks can be leveraged to design
straightforward yet powerful controllers able to fully manipulate cluster
synchronization of a generic network, thus shaping at will its parallel
functioning. Specifically, we demonstrate how to induce the formation of
spectral blocks in networks where such structures would not exist, and how to
achieve precise mastering over the synchronizability of individual clusters by
dictating the sequence in which each of them enters or exits the
synchronization stability region as the coupling strength varies. Our results
underscore the pivotal role of cluster synchronization control in shaping the
parallel operation of networked systems, thereby enhancing their efficiency and
adaptability across diverse applications.
