While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have
become a major tool in numerical analysis of partial differential equations.
This monograph considers problems of optimal control for partial differential equations of elliptic and, more importantly, of hyperbolic types on networked domains. The main goal is to describe, develop and analyze iterative space and time domain decompositions of such problems on the infinite dimensional level.