Abstract
A control problem for a partially observed linear stochastic system with an exponential quadratic cost functional is formulated and explicitly solved. It is assumed given that the estimation of the state is described by the solution of the information filter which is known. This solution is a sufficient statistic for the unknown state based on the observations. In this paper an optimal control is determined explicitly in a simple, direct manner from this sufficient statistic. This approach does not use either the solution of a Hamilton-Jacobi-Bellman equation or a stochastic maximum principle with backward stochastic differential equations. This control problem is often called a linear partially observed risk sensitive control problem.
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