On statistical risk functional in a control problem for an object moving in a conflict environment

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Abstract

A statistical criterion is suggested for a variational problem on constructing an optimal trajectory of evasion of a movable object from detection by a stationary observer. Coordinates of the observer are assumed to be not known exactly but are distributed in the space in accordance with some a priori known probability distribution. The risk functional for the variational problem is taken to be expectation of an integral loss functional (depending on a random parameter) in the deterministic problem, which is calculated in this work.

Original Russian Text © M.E. Shaikin, 2011, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2011, No. 1, pp. 22–31.