Scaled Consensus Over a Network of Wave Equations

In this article, the scaled consensus issue for a network of wave partial differential equations is investigated in a directed communication setting, where the agent states approach the dictated ratios. To this end, a distributed protocol is proposed for the considered system. Then, a Lyapunov function is constructed to ensure scaled consensus, wherein the properties of algebraic connectivity are employed to handle the asymmetric interaction matrix. Using tools from semigroup theory, the well-posedness of the underlying system is guaranteed. Moreover, we extend the derived results to a leader-following scaled consensus scenario. Numerical examples are presented to support the proposed setup.