Outer synchronization for general weighted complex dynamical networks considering incomplete measurements of transmitted information

Abstract

Outer synchronization for general weighted complex dynamical networks with randomly incomplete measurements of transmitted state variables is studied in this paper. The incomplete measurements of control information, always occurring during the transmission, should be considered seriously since it would cause the failure of outer synchronization process. Different from previous methods, we develop a new method to handle the incomplete measurements, which cannot only balance well the overly deviated controllers affected by the incomplete measurements, but also has no particular restriction on the node dynamics. Using the Lyapunov stability theory along with the stochastic analysis method, sufficient criteria are deduced rigorously to obtain the adaptive control law. Illustrative simulations are given to verify that our proposed controllers are effective and efficient dealing with the incomplete measurements.