On differential games with geometric and integral constraints

TitleOn differential games with geometric and integral constraints
Publication TypeJournal Article
Year of Publication2014
AuthorsBelousov, AA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.02.038
Issue2
SectionInformation Science and Cybernetics
Pagination38-44
Date Published2/2014
LanguageRussian
Abstract

The paper deals with the problem of bringing a trajectory of the linear conflict-controlled process to a linear subspace in the case of general convex integral constraints on the players’ controls. Sufficient conditions for the problem solvability in the class of measurable controls are obtained. In so doing, the technique of set-valued mappings and convex analysis (epigraph of a function, recession cone) is used. It is shown how to investigate the game with geometric constraints by the developed method.

Keywordsdifferential games, geometric constraints, integral constraints
References: 

1. Pontryagin L. S. Chosen scientific works. T. 2. – Moscow: Science, 1988. – 576 p.
2. Nikolsky M. S. Direct method in linear differential games with integral constraints. In: Managed systems. Iss. 2. Novosibirsk: Izd-vo SO AN USSR, 1969: 49–58.
3. Nikolsky M. S. Dif. uravneniia, 1972, 8, No. 6: 964–971 (in Russian).
4. Nikolsky M. S. Dif. uravneniia, 1992, 28, No. 2: 219-223 (in Russian).
5. Chikry A. A. Conflict-driven processes. Kyiv: Nauk. dumka, 1992 (in Russian).
6. Rokafellar R. Convex analysis. Moscow: Mir, 1973 (in Russian).
7. Belousov A. A. Pulse controls in differential games with integral constraints. In: Theory of optimal solutions. Kyiv: V. M. Glushkov Institute of Cybernetics of NAS of Ukraine, 2013: 50–55 (in Ukrainian).
8. Oben J. P., Ekland I. Applied nonlinear analysis. Moscow: Mir, 1988 (in Russian).
9. Kisielewicz M. Differential inclusions and optimal control. In: Mathematics and Its Applications, Dordrecht: Kluwer, 1991, 44.