Synchronization of a Network of Nonlinear Plants with Time Delay as in Condition Under Uncertainty

Abstract

Robust algorithms for synchronizing a network of nonlinear plants with time delay are proposed. A network of control plants in the Lurie form with Lipshets nonlinearities is considered taking into account the time delay under the conditions of constantly operating external uncontrolled disturbances. Taking into account nonlinear and delayed components in mathematical models of plants makes the system close to real. In each local network plant, the input of the leading subsystem is monitored. Dynamic compensation of disturbances in each of the plants is carried out by extracting a signal that carries information about these disturbances, and then suppressing it using an auxiliary circuit and two observers of the system variables. The use of variable observers is due to the need to obtain estimates of the derivatives of the system variables, the measurement of which is not available. A numerical example of the synchronization of a network consisting of four nonlinear control plants with a delay in state under conditions of uncertainty of the parameters of their mathematical models and the action of external bounded disturbances is considered. For the network of plants, the proposed control algorithms are applied. The numerical simulation in the Simulink Matlab package was carried out, the graphs of transient processes for tracking errors for each of the four subsystems are presented. The simulation results confirmed the theoretical conclusions and showed good performance of the proposed synchronization algorithms in the conditions of constantly operating external and internal disturbances.