Control theory is applied to the problem of routing a vehicle from one point to another in fixed time. The method requires an initial guess at the route, which is then gradually warped into a route that is locally optimal. Application is made to a problem where a submarine wishes to find a route along with minimal qradiated noise will be intercepted by the enemy. Certain tactical problems take the form of inquiries into the best way of getting from A to B, where A and B are positions in a continuous state space. The optimal route from A to B is not necessarily a straight line: ocean currents or winds may cause a ship to be routed indirectly to take advantage of favorable areas, or certain regions may be threatening (thyphoons, enemy units) or even non-feasible (land). A 'route' being a complicated mathematical object, it should be expected that the time required for computation of an optimal route will be significant, and that it will be sensitive to the way in which the optimal routing problem is formulated and solved. This technical report describes a somewhat unconventional approach to formulation and solution. It includes a program demonstrating technique in a problem where a submarine is to be routed past several listeners trying to detect it.
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