A problem of program maximin with constraints of asymptotic nature

A. G. Chentsov ; I. I. Savenkov ; Yu. V. Shapar'

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 91-110

Résumé

We consider a linear game control problem for maximin with asymptotic constraints, which naturally arise in connection with the realization of “narrow” control pulses. In terms of content, this corresponds to pulsed control modes with full fuel consumption. The emerging game problem corresponds to the use of asymptotic control modes by both players, which is reflected in the expansion concept realized in the class of finitely additive measures. The original content control problem for each of the players is considered as a variant of abstract formulation related to attainability under asymptotic constraints, for which the corresponding generalized attainability problem is constructed and the representation of the attraction set playing the role of an asymptotic analogue of an attainability domain in the classical control theory is established. This concretization is realized for each of the players, on the basis of which a generalized maximin is obtained, for which a variant of the asymptotic realization in the class of ordinary controls is indicated. A “finite-dimensional” description of the attraction set is obtained, which makes it possible to find maximin using numerical methods. The solution of a model example of the problem of game interaction of two material points, including the stage of computer modeling, is considered.

Détail

Keywords: finitely additive measure, attainability domain, linear control system.