A separation theorem for stochastic control problems with point-process observations

Abstract

The exact solution is derived for a stochastic optimal control problem involving a linear stochastic plant, quadratic costs, and nonlinear, nongaussian observations. The observations are in the form of a point process in which each point has both a temporal and a spatial coordinate. The state of the stochastic plant influences the intensity of the observed time-space point process. The solution to this dual control problem can be realized with a separated estimator-controller in which the estimator is nonlinear, mean-square optimal, and finite dimensional, and the controller is the certainty equivalent linear controller. Motivation for the stochastic optimal control problem studied here is given in terms of position sensing and tracking for quantum-limited optical communication problems.