The Use of the Integral Functional in Some Methods of Control in the Presence of Small Random Perturbations

The problems described in [1] and [2] (parametric control and control by means of a single switching) are considered with the difference that the characterizing function is replaced by the characterizing functional of the integral type. In both cases we prove the existence of the minimum of the variance of some functional and evaluate this minimum. The minimizing functions are also determined. Necessary and sufficient conditions for this minimum to be equal to zero are given.