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 theith team member at timekis an affine function of both the one-step predicted Kalman filter estimate and theith team member's observation at timek. 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.