Max-plus enabled dynamic programming for sensor platform tasking

In a military context, the value of a future operation is obtained as the expectation of the payoff, based on the current probability distributions describing our knowledge of the battlespace state. Sensing vehicles may be employed to improve this value function through control of the observation-conditioned distribution. We consider the problem of tasking sensing vehicles so as to optimize the future value. Max-plus based dynamic programming was employed, exploiting the special form of the value function as a pointwise maximum of linear functionals, where we note that this form is preserved as one propagates. This approach avoids the curse-of-dimensionality, but encounters another computational complexity difficulty. This complexity growth is attenuated through projection onto lower-dimensional subspaces. An error analysis is developed for these approximations.