The dynamic linear exponential Gaussian team problem

The dynamic team problem for a linear system with Gaussian noise, exponential of a quadratic performance index, and one-step delayed sharing information pattern is considered. It is shown, via dynamic programming, that the multistage problem can be decomposed into a series of static team problems. Moreover, the optimal policy of the
i
th team member at time
k
is an affine function of both the one-step predicted Kalman filter estimate and the
i
th team member's observation at time
k
. Efficient algorithms are available for determining the gains of this affine controller. This model and solution are applied to an approximate resource allocation problem associated with a defense network, and a numerical example is discussed.