Application of the Theory of Optimal Control to the Development of Terminal Search Patterns.

摘要

The theory of optimal search, as usually presented, treats the development of a search effort allocation over a space X which is optimal in some sense, given an underlying target position distribution. In other words, when the location of a target is not precisely known and when the detection characteristics of the search mechanism are well-defined, one can prescribe a search effort function of both space and time to achieve a practical MOE (measure of effectiveness). The best measure of effectiveness is usually considered to be the probability of detection, or target acquisition, under a time budget constraint. Optimal search theory, surprisingly, usually does not embrace in a rigorous, methodical fashion the generation of vehicle path processes which reproduce, to some level of approximation, the optimal allocation of effort. Rather, more often than not, heuristic search mechanism, such as parallel sweeping or radial tracking, are designed to replicate the effort distribution. The purpose of the report is primarily to examine, from first principles, the underlying variational problems and to obtain, if possible, the best solutions satisfying reasonable cost criteria. We show that it is possible to generate sensible paths when one knows that the target is stationary. Also, those conditions under which the best solution can be approximated by a logarithmic spiral are presented. Finally, in the case of a moving target, we present a stochastic vehicle search pattern, whose expected path, for example, could be followed by a search vehicle.