Relative value of measurements in a discrete decentralized LQG framework

A discrete linear multi-agent system is considered, and each agent in the system aims to minimize his own infinite-horizon quadratic cost. An attempt is made to quantify the relative value of information at each node in the network. This knowledge is relevant when the exchange of information between agents is costly or limited. First, a centralized approach to the estimation and control problem is taken. Then, a nonzero sum game is formulated, in which the strategies are the measurements selections. We impose that these be time periodic, which allows us to pose an equivalent finite-horizon game and to interpret the results as explicit data rates. The method is applied to the simple example of a string of cars, and provides an interesting validation to a heuristic assumption made in previous work on string stability.