Preassigned-time control for cluster synchronization of multi-layer networks via partial state components

This paper focuses on the cluster synchronization of multi-layer networks (MLNs) with intra-layer coupling and inter-layer coupling due to the network scale and dynamic clustering of MLNs. Recognizing that not all nodal states can be synchronized in practice, this paper introduces partial component synchronization. An efficient preassigned-time (PDT) control scheme is designed with parameters that can be adjusted freely based on the MLN states to achieve control objectives. The PDT cluster synchronization conditions for MLNs are obtained and a rigorous theoretical proof is provided according to the Lyapunov stability theory. Moreover, the settling time of PDT cluster synchronization is independent of the initial values and parameters, and can be preassigned arbitrarily. Numerical simulations are presented to validate the theoretical results and demonstrate the feasibility of the proposed control method.