Synchronization controller design for a network of boundary-controlled anti-stable wave equation with time-varying perturbations

Abstract

In this paper, a output feedback controller based on an infinite dimensional disturbance observer and a state feedback controller based on backstepping method are proposed to solve the synchronous control problem of network anti-stable wave equation with time-varying disturbance at the boundary. One agent in the network wave equation as the virtual leader, and all remaining agents need to track the status of the virtual leader incrementally. Here, the design of synchronous controller is divided into three parts. Firstly, backstepping method is used to design a set of controllers that makes all the systems stable. Secondly, infinite dimensional disturbance observers based on the idea of the active disturbance rejection control (ADRC) technology are used to estimate the disturbance. Finally, the synchronization controllers are designed, and the error between the following system and the virtual leader system converges to 0 in the appropriate sense. The applicability of the closed-loop system is analyzed and proved. The simulation results show the effectiveness of the controller design.