A Target Recognition Problem: Sequential Analysis and Optimal Control

An iterative computational method for determining the value function of an optimal control problem, related to target tracking, is presented. The target is assumed to be located in a fixed known position in space, but its identity (hostile or friendly) is known only with a prior probability. An observation of the target can be made at any location, and its error has position-dependent probability. The objective is finding the optimal navigation and observation strategy which leads to a final decision (i.e., the target is friendly or hostile), The value function is shown to be the unique viscosity solution of a variational inequality Furthermore it is the unique fixed point of a nondecreasing concave operator.