Optimal decentralized control of coupled subsystems with control sharing

The optimal decentralized control of coupled subsystems with control sharing is investigated. The system consists of n-coupled subsystems, each with a local control station. The evolution of a subsystem is controlled by the actions of all control stations. However, each control station observes only the state of its subsystem and the one-step delayed actions of all control stations. At each time, a cost that depends on the state of all subsystems and the actions of all control stations is incurred. The system has non-classical information structure; since each control station observes the delayed control actions of all other control stations, the system is said to have control-sharing information structure. We use the approach of Mahajan et al. (2008), to obtain the structure of optimal control stations and a dynamic programming decomposition, which is similar to the dynamic program for centralized partially observed systems. The structure of optimal control stations is simpler than the general structure proposed in Mahajan et al. (2008), and, consequently, so is the dynamic programming decomposition.