Abonnement à la biblothèque: Guest
Journal of Automation and Information Sciences

Publication de 12  numéros par an

ISSN Imprimer: 1064-2315

ISSN En ligne: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

Indexed in

On Nonstationary Problem of Motion Control in Conflict Situation

Volume 51, Numéro 7, 2019, pp. 55-66
DOI: 10.1615/JAutomatInfScien.v51.i7.50
Get accessGet access

RÉSUMÉ

The mathematical theory of control under conflict and uncertainty provides a wide range of fundamental methods to study controlled dynamic processes of various nature. This paper considers the game problems of pursuit for nonstationary controlled processes of general type with a cylindrical terminal set. The investigation is closely related to L.S. Pontryagin first direct method and the method of resolving functions. The purpose of the paper is to derive sufficient conditions for the game termination for some guaranteed time in favor of the first player to provide the control implementing this result. In the development of the method of resolving functions the upper and lower resolving functions of two types are introduced in the form of support functions of special multivalued mappings. This made it possible to obtain conditions for the game termination in the class of quasi- and stroboscopic strategies. The comprehensive analysis of properties of special maltivalued mappings and their selectors allowed us to choose measurable controls by virtue of measurable choice theorem. A comparison of the guaranteed times of the above mentioned methods is given. In so doing the properties of L × B -measurability of the key multivalued mappings and the corresponding resolving functions − the support functions of these mappings are used. The property of superpositional measurability of above mentioned objects plays essential role in the method design. As a rule, in specific model examples the resolving functions are the large positive roots of certain quadratic equations that makes it possible to obtain solution in an analytical form.

RÉFÉRENCES
  1. Pontryagin L.S., Selected scientific papers [in Russian], Nauka, Moscow, 1988. .

  2. Chikrii A.A., Conflict controlled processes, Springer Science and Business Media, Boston, London, Dordrecht, 2013. .

  3. MordukhovichB.S., Variational analysis and generalized differentiation. I.Basic Theory, 330, II. Applications, 331, Springer, Berlin, Heidelberg, New York, 2006. .

  4. PolovinkinE.S., Multivalued analysis and differential inclusions [in Russian], Fizmatlit, Moscow, 2014. .

  5. Lokk A.S., Projectiles control [in Russian], GITTL, Moscow, 1957. .

  6. Chikrii A.A., An analytical method in dynamic pursuit games, Proceedings of the Steklov Institute of Mathematics, 2010, 271, 69-85. .

  7. Chikrii A.A., Belousov A.A., On linear differential games with integral constraints, Trudy Instituta matematiki i mekhaniki UrO RAN, 2009, 15, No. 4, 290-301. .

  8. Chikrii A.A., Differential games with some pursuers, Banach Center Publications, 1985, 14, No. 1, 81-107. .

  9. Chikrii A.A., Multivalued mappings and their selections in game control problems, Journal of Automation andlnformation Sciences, 1995, 27, 27-38. .

  10. PittsykM., ChikriiA.A., On a group pursuit problem, J. of Applied Mathematics and Mechanics. 1982, 46, No. 5, 584-589. .

  11. Aubin J.-P., Frankowska H., Set-valued analysis, Birkhauser, Boston, Basel, Berlin, 1990. .

  12. Krasovskiy N.N., Game problems on contact of motions [in Russian], Nauka, Moscow, 1970. .

  13. Hajek O., Pursuit games, Academic Press, New York, 1975,12. .

  14. Aumann R.J., Integrals of set-valued functions, J. Math. Anal.Appl., 1965,12, 1-12. .

  15. Filippov A.F., Differential equations with discontinuous right-hand side [in Russian], Nauka, Moscow, 1985. .

  16. Chikrii A.A., Chikrii V.K., Image structure of multivalued mappings in game problems of motion control, Journal of Automation and Information Sciences, 2016, 48, No. 3, 20-35. .

  17. Pepelyaev V.A., Chikrii A1.A., On the game dynamics problems for nonstationary controlled processes, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy uprabvleniya i informatiki", 2017, No. 2, 7-16. .

  18. Nakonechnyi A.G., Mashchenko S.O., Chikrii V.K., Motion control under conflict condition, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya i informatiki", 2018, No. 1, 53-71. .

  19. Baranovska L.V., Method of resolving lunctions for the differential-difference pursuit game for differentinertia objects, Studies in Systems, Decision and Control, 2016, 69, 159-176. .

  20. Chikrii A.A., Chikrii G.Ts., Matrix resolving functions in game problems of dynamics, Proceedings ofthe Steklov Institute ofMathematics, 2015, 291, Suppl. 1, 56-65. .

  21. Chikrii G.Ts., Using the effect of information delay in differential pursuit games, Cybernetics and Systems Analysis, 2007, 43, No. 2, 233-245. .

  22. ChikriiA.A., Chikrii G.Ts., Volyanskiy K.Y., Quasilinear positional integral games of approach, Journal ofAutomation and Information Sciences, 2001, 33, No. 10, 31-43. .

  23. Chikrii A.A., Dzyubenko K.G., Bilinear Markov processes of searching for moving objects, Problemy upravleniya i informatiki, 1977, No. 1, 92-107. .

  24. Chikrii A.A., Eidelman S.D., Game problems for fractional quasilinear systems, Int. Journal Computers and Mathematics 'with Applications, Pergamon, 2002, 44, 835-851. .

  25. Pilipenko Yu.V., Chikrii A.A., Oscillatory conflict-controlled processes, Prikladnaya matematika i mekhanika, 1993, 57, No. 3, 3-14. .

  26. Chikrii A.A., Game dynamic problems for systems with fractional derivatives, Springer Optimization and its Applications, 2008, 17, 349-387. .

  27. Chikrii A.A., Eidelman S.D., Game control problems for quasi-linear systems with Riemann- Liouville fractional derivatives, Kibernetika i sistemnyi analiz, 2001, No. 6, 66-99. .

  28. Chikrii A.A., The problem of avoidance for controlled dynamic objects, Int. J. Game Theory and Applications, 1997, 3, 7-20. .

Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections Prix et politiques d'abonnement Begell House Contactez-nous Language English 中文 Русский Português German French Spain