Abstract
The situation considered is of optimally controlling a deterministic system from a given state to an initially unknown targety in a fixed time interval [T0,T]. The target will be certainly known at a random time τ in [T0,T]. The controller knows the distributions ofy and τ. We derive the Bellman equation for the problem, prove a verification theorem for it, and demonstrate how the distribution τ influences the optimal control. We show that, in the linear-quadratic case, the optimal control is given by a feedback law that does not depend on the distribution of τ.
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