In this paper, we investigate a distributed predictive control and estimation problem with information structured constraints. A system with information structures is defined as a system in which each subsystem collects spatio-temporally different information, and in general it is necessary to collect and process information in a distributed fashion. We propose a distributed predictive control and estimation laws with local information that each distributed subsystem obtains. The effectiveness of a proposed control and estimation law is demonstrated through a numerical simulation of smart grid.