Consensus of wave PDE agents under switching graphs

Abstract

We investigate the consensus problem for a network of infinite-dimensional agents with directed switching topology. Different from the general parabolic-type agents, networked wave PDEs which are suitable to model a group of flexible spacecrafts are addressed in this paper. Under mild conditions, a boundary control protocol is proposed for the underlying system. Subsequently, a novel common Lyapunov function is constructed to guarantee consensus and detailed analysis of theoretical findings is obtained. The well-posedness is further considered with the help of semigroup theory and inductive method. Moreover, a numerical example is exhibited to support the derived results.