Optimal information acquisition for a linear quadratic control problem

This paper develops a generalization of the linear quadratic control problem with partial information. As in the standard partial information setting, it is assumed that the state variable is only observed with noise. The idea in this paper is that the information level may be chosen optimally. In real life information is costly to acquire. It is therefore a trade off between the costs of getting detailed information and the increased value this information gives. We believe that the technique we present should have potential for application within both economics and engineering.