An Approximation Technique for Small Noise Open Loop Control Problems.

This paper is concerned with the development of an approximation technique for the solution of a class of fixed stopping time small noise open loop control problems. These problems arise by adding an additive white noise term with a small coefficient sq rt 2 epsilon I to the system equations in the deterministic control problem. An approximation scheme is developed that has the advantage that one finds approximately optimal controls simultaneously for all sufficiently small epsilon. The scheme requires the solution of a generalized linear regulator problem which is solvable easily numerically. The numerical method is also presented. Author