Disturbances compensation in nonlinear dynamical networks with communication delay

The paper deals with the robust algorithm of synchronization of dynamical networks with communication time delay, where each agent (subsystem) is described by nonlinear differential equation under unknown parameters and external uncontrollable bounded disturbances. The control algorithm is designed by using so called method of auxiliary loop. According to the method of auxiliary loop we introduce the nominal plant with desired parameters parallel to each agent. The difference between the output of the agent and the output of the auxiliary loop gives a function which depends on parametric and external disturbances. Then this function is used in the control law for compensation of disturbances. The proposed algorithm provides the network synchronization and compensation of uncontrollable disturbances with a required accuracy. Analytical results are presented by networks consisting of four nodes and fifty pendulums.