Control problems with random and progressively known targets

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 in [T₀,T]. The controller knows the distributions ofy and . We derive the Bellman equation for the problem, prove a verification theorem for it, and demonstrate how the distribution 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 .The author wishes to express his gratitude to Prof. Wendell H. Fleming and Prof. Steven Orey for fruitful discussion concerning this work.This research was supported in part by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation.