Leader-follower synchronization controller design for a network of boundary-controlled wave PDEs with structured time-varying perturbations and general disturbances

A feedback controller based on an infinite dimensional observer is proposed to solve the synchronous control problem of network wave equations with time-varying and general perturbations at the boundary. An agent in the network as a virtual leader, and all remaining agents need to incrementally track the status of the virtual leader and each agent is controlled by the Neumann-type drive through the boundary. In this paper, by adopting the idea of the active disturbance rejection control (ADRC) technology, the design of the synchronous controller is divided into three parts and has various functions in this paper. Firstly, it compensates the total disturbance asymptotically. Secondly, it ensures the asymptotic convergence between the network state and the virtual leader state to track the virtual leader. Finally, it ensures that the paired states are synchronized. The convergence of infinite dimensional systems and the suitability of closed-loop systems are analyzed and proved. Three network wave equations with disturbance observer feedback control are simulated numerically, and the simulation results show the effectiveness of the proposed method.