Distributed Prescribed-Time and Adaptive Synchronization of Complex Dynamical Networks under Directed Topologies

This paper addresses an adaptively distributed prescribed-time synchronization problem of complex dynamical networks (CDNs) via distributed pinning control schemes using neighboring information over the digraph. The novel distributed prescribed-time synchronization pinning control algorithms with static and dynamic coupling laws are developed to achieve global synchronization in the specified time, where each node can adjust its strategy on its procurable synchronization error. Based on the time transformation method and Lyapunov analysis theory, it is proved that global synchronization can be guaranteed in a pre-defined time and moreover, this synchronization can be preserved after the time, and further the control inputs are kept uniformly bounded. Lastly, the numerical simulation results are further presented to illustrate the effectiveness of the developed synchronization control methods.