Abstract
This paper supplies an intuitive probabilistic interpretation of the necessary conditions on locally optimal solutions of the optimization problems treated in „Optimal Navigation with Random Terminal Time in the Presence of Phase Constraints” by means of a functional analytic approach. The dynamic programming approach yields rigorous results only under restrictive and hard-to-verify assumptions on the cost function, but it follows an interpretation of an optimal control as direction of fastest fecrease of the conditional expected residual costs.
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