Stochastic Descriptor Pursuit Game

A differential pursuit game in a stochastic descriptor linear system is analyzed. The dynamic of the system is described by Ito’s stochastic differential algebraic equation. Solutions of the equation are presented by the stochastic formula of the variation of constants in terms of the initial data and control unit. Constraints on the support functionals of two sets defined by the behaviors of the pursuer and evader are used to obtain the game completion conditions. The method of resolving functions is applied to construct pursuer’s control bringing the dynamic vector of the system to the terminal set. The results are illustrated by an example of a stochastic descriptor system that describes transients in a radio engineering filter with random disturbances in the form of white noise.