ИККИНЧИ ТАРТИБЛИ ДИФФЕРЕНЦИАЛ ЎЙИНЛАР

457

Мақолада ҳаракатланувчи объектларнинг бошланғич ҳолатлари ва бошланғич тезликлари чизиқли боғлиқ ҳамда бошқарувлари геометрик чегараланишга эга ҳол учун иккинчи тартибли дифференциал
ўйинларда қувиш-қочиш масаласи ўрганилган. Бунда қувувчи ва қочувчи учун янги етарлилик шартлари таклиф қилинган.

Журнал номиFarDU Ilmiy Xabarlari
Нашр номи2019-4
Кўришлар сони 457

Internet ҳавола

DOI

UzSCI тизимида яратилган сана 16-08-2022

Ўқишлар сони 0

Нашр санаси 04-11-2019

Мақола тилиO'zbek

Саҳифалар сони13-19

Калит сўзлар

дифференциал ўйин

қочувчи

тезланиш

геометрик чегараланиш

қувловчи

бошланғич ҳолат

Ўзбек

Мақолада ҳаракатланувчи объектларнинг бошланғич ҳолатлари ва бошланғич тезликлари чизиқли боғлиқ ҳамда бошқарувлари геометрик чегараланишга эга ҳол учун иккинчи тартибли дифференциал
ўйинларда қувиш-қочиш масаласи ўрганилган. Бунда қувувчи ва қочувчи учун янги етарлилик шартлари таклиф қилинган.

Калит сўзлар

дифференциал ўйин

қочувчи

тезланиш

геометрик чегараланиш

қувловчи

бошланғич ҳолат

Русский

В настоящей статье изучается задача преследования-убегания для дифференциальных игр второго порядка, когда начальные состояния и начальные скорости игроков линейно зависимы при геометрических
ограничениях на управления. Получены новые достаточные условия разрешимости для задач преследования и убегания.

Калит сўзлар

преследователь

убегающий

Дифференциальная игра

геометрическое ограничение

ускорение

начальные состояния

English

In this paper, we study the pursuit-evasion problem for the second order differential game when the initial positions of moving objects are linearly dependent and controls of the players have geometric constraints. The new
sufficient solvability conditions are obtained for problems of the pursuit and evasion.

Калит сўзлар

acceleration

evader

pursuer

differential game

geometric constraint

initial positions

№ Муаллифнинг исми Лавозими Ташкилот номи

1 samatov B.T. 1 Namangan state university

2 Soyibboev U.B. 2 Namangan state university

3 Mirzamahmudov U.A. 3 Namangan state university

№ Ҳавола номи

1 1. Azamov A.A., About the quality problem for the games of simple pursuit with the restriction (in Russian), Serdika. Bulgarian math.spisanie, 12, 1986, -P. 38-43.

2 2. Azamov A.A., Samatov B.T. П-Strategy. An Elementary introduction to the Theory of Differential Games. - T. : National Univ. of Uzb., 2000. – P. 32.

3 3. Azamov A.A., Samatov B.T. The П-Strategy: Analogies and Applications, The Fourth International Conference Game Theory andManagement , June 28-30, 2010, St. Petersburg, Russia,Collected papers. - P.33-47.

4 4. Azamov A., Kuchkarov A.Sh. Generalized 'Lion Man' Game of R.Rado, Contributions to game theory and management. Second International Conference "Game Theory and Management" -St.Petersburg, Graduate School of Management SPbU. - St.Petersburg, 2009. - Vol.11. - P. 8-20.

5 5. Azamov A.A., Kuchkarov A.Sh., Samatov B.T. The Relation between Problems of Pursuit,Controllability and Stability in the Large in Linear Systems with Different Types of Constraints, J.Appl.Maths and Mechs. -Elsevier. - Netherlands, 2007. - Vol. 71. - N 2. - P. 229-233.

6 6. Barton J.C, Elieser C.J. On pursuit curves, J. Austral. Mat. Soc. B.- London, 2000. - Vol.41.- N 3. - P. 358-371.

7 7. Borovko P., Rzymowsk W., Stachura A.Evasion from many pursuers in the simple case, J. Math. Anal.AndAppl. - 1988. - Vol.135. - N 1. - P. 75-80.

8 8. Chikrii A.A., Conflict-controlled processes, Boston-London-Dordrecht: Kluwer Academ. Publ., 1997, 424 p.

9 9. Fleming W. H. The convergence problem for differentialgames, J.Math. Anal. Appl. - 1961. - N 3. - P. 102-116.

10 10. A. Friedman, Differential Games, New York: Wiley, 1971, 350 p.

11 11. Hajek O. Control Theory in the Plane (Lecture Notes in Control and Information Sciences) - Berlin, New York: Springer-Verlag, 2009. - 220 p.

12 12. Hajek O. Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion. - NY.: Dove. Pub. 2008. - 288 p.

13 13. Isaacs R., Differential Games, J. Wiley, New York-London-Sydney, 1965, 384 p.

14 14. Ibragimov G.I. Collective pursuit with integral constrainson the controls of players, Siberian Advances inMathematics, 2004, v.14,No.2,p.13-26.

15 15. Ibragimov G.I. AbdRasid N., Kuchkarov A., Fudziah Ismail. Multi Pursuer Differential Game of Optimal Approach with Integral Constraints, Taiwanese Journal of Mathematics, 2015. - Vol. 19. - No 3. - P. 963-976.

16 16. Ibragimov G.I., Azamov A. A., Khakestari M. Solution of a linear pursuit-evasion game with integral constraints, ANZIAM Journal.Electronic Supplement.- 2010. - Vol.52. - P. E 59-E 75.

17 17. Imado F. Some practical approaches to pursuit-evasion dynamic games, CSA. - Elsevier, 2002. - Vol.38(2). - N 3. - P. 26-37.

18 18. Krasovskiy. A. N., Choi Y. S. Stochastic Control with the Leaders-Stabilizers. - Ekaterinburg : IMM Ural Branch of RAS,2001. - 51 p.

19 19. Krasovskii A. N., Krasovskii N. N. Control lunder Lack of Information. - Berlin etc. :Birkhauser, 1995. – 322, p.

20 20. Kuchkarov A.Sh. Solution of Simple Pursuit-Evasion Problem When Evader Moves on a Given Curve, International Game Theory Review. - World Scientific Publishing Company, 2010. - Vol.12. - N 3, p. 223-238.

21 21. Miller B., Rubinovich E.Y. Impulsive Control inContinuous and Discrete-Continuous Systems. - N.Y. : KluwerAcademic/Plenum Publishers, 2003. - 447 p.

22 22. Nahin P.J. Chases and Escapes: The Mathematics of Pursuit and Evasion. Princeton University Press, Princeton, 2012, - 260.

23 23. Petrosyan L. A. About some of the family differential gamesat a survival in the space Rn (in Russian), Dokl.Akad.Nauk SSSR, 1965, 161, No1, p.52-54.

24 24. Petrosyan L.A. The Differential Games of pursuit (in Russian), Leningrad, LSU, 1977, 224 p.

25 25. Petrosyan L.A., Rikhsiev B.B. Pursuit on the plane (in Russian), Nauka, Moscow, 1991, 96 p.

26 26. Petrosyan L.A., Mazalov V.V. Game Theory and Applications I, II, New York: Nova Sci. Publ., 1996, 211 p., 219 p.

27 27. Petrosyan L.A. Pursuit. Games with "a Survival Zone" (in Russian), Vestnic Leningard State Univ., 1967, No.13, p.76-85.

28 28. Petrosyan L.A., Dutkevich V.G. Games with "a Survival Zone", Occation L-catch (in Russian), Vestnic Leningrad State Univ.,1969, No.13, v.3, p.31-38.

29 29. Pontryagin L.S. "Linear Differential Pursuit Games" (in Russian), Math. Sb. [Math.USSR-Sb], 112, No.3, p.307-330.

30 30. Pshenichnyi B.N. The simple pursuit with some objects (in Russian), Cybernetics, 1976, No.3, pp.145-146.

31 31. Rikhsiev B.B. The differential games with simple motions (in Russian), Tashkent: Fan, 1989, 232 p.

32 32. Satimov N.Yu. Methods of solving of pursuit problem in differential games (in Russian), Tashkent: NUUz, 2003, 245 p.

33 33. Samatov B.T. The construction of the П-strategy for thegame on simple pursuit with integral constraints (in Russian). The boudary value problems for non-classical mathematical-physical equations. Tashkent: Fan, 1986, p. 402- 412.

34 34. Samatov B.T. The Differential Game with "A Survival Zone" with Different Classes of Admissiable Control Functions. Game Theory and Applications. Nova Science Publ. 2008.V.13.P.143-150.

35 35. Samatov B.T. The Game with "A Survival Zone" in the caseintegral-geometric constraints on the controls of the Pursuer, Uzb.Math.jornal - Tashkent, 2012. - No 7. - p. 64-72.

36 36. Samatov B.T. On a Pursuit-Evasion Problem under a Linear Change of the Pursuer Resource, Siberian Advances in Mathematics. –Allerton Press, Inc. Springer. - New York, 2013. - Vol. 23. - No 4. - P.294-302.

37 37. Samatov B.T. The Pursuit-Evasion Problem under Integral-Geometric constraints on Pursuer controls, Automation and Remote Control. - Pleiades Publishing, Ltd. - New York, 2013. -Vol. 74. - No 7. - P. 1072-1081.

38 38. Samatov B.T. The Resolving Functions Method for the Pursuit Problem with Integral Constraints on Controls, Journal of Automation and Information Sciences. - Begell House, Inc. (USA). 2013. - Vol. 45, No 8. - P.41-58.

39 39. Samatov B.T. The П-strategy in a differential game with linear control constraints, J. Appl. Maths and Mechs. - Elsevier. - Netherlands,2014. - Vol. 78. - No 3. - P. 258-263.

40 40. Samatov B.T. Problems of group pursuit with integral constraints on controls of the player. I, Cybernetics and Systems Analysis.–Springer International Publishing AG. - Switzerland, 2013. - Vol.49. - No5. - P.756-767.

41 41. Samatov B.T. Problems of group pursuit withintegral constraints on controls of the player. II, Cybernetics andSystems Analysis.–Springer International Publishing AG -Switzerland, 2013. - Vol. 49. - No 6. - P.907-924.

Кутилмоқда

№	Муаллифнинг исми	Лавозими	Ташкилот номи
1	samatov B.T.	1	Namangan state university
2	Soyibboev U.B.	2	Namangan state university
3	Mirzamahmudov U.A.	3	Namangan state university

№	Ҳавола номи
1	1. Azamov A.A., About the quality problem for the games of simple pursuit with the restriction (in Russian), Serdika. Bulgarian math.spisanie, 12, 1986, -P. 38-43.
2	2. Azamov A.A., Samatov B.T. П-Strategy. An Elementary introduction to the Theory of Differential Games. - T. : National Univ. of Uzb., 2000. – P. 32.
3	3. Azamov A.A., Samatov B.T. The П-Strategy: Analogies and Applications, The Fourth International Conference Game Theory andManagement , June 28-30, 2010, St. Petersburg, Russia,Collected papers. - P.33-47.
4	4. Azamov A., Kuchkarov A.Sh. Generalized 'Lion Man' Game of R.Rado, Contributions to game theory and management. Second International Conference "Game Theory and Management" -St.Petersburg, Graduate School of Management SPbU. - St.Petersburg, 2009. - Vol.11. - P. 8-20.
5	5. Azamov A.A., Kuchkarov A.Sh., Samatov B.T. The Relation between Problems of Pursuit,Controllability and Stability in the Large in Linear Systems with Different Types of Constraints, J.Appl.Maths and Mechs. -Elsevier. - Netherlands, 2007. - Vol. 71. - N 2. - P. 229-233.
6	6. Barton J.C, Elieser C.J. On pursuit curves, J. Austral. Mat. Soc. B.- London, 2000. - Vol.41.- N 3. - P. 358-371.
7	7. Borovko P., Rzymowsk W., Stachura A.Evasion from many pursuers in the simple case, J. Math. Anal.AndAppl. - 1988. - Vol.135. - N 1. - P. 75-80.
8	8. Chikrii A.A., Conflict-controlled processes, Boston-London-Dordrecht: Kluwer Academ. Publ., 1997, 424 p.
9	9. Fleming W. H. The convergence problem for differentialgames, J.Math. Anal. Appl. - 1961. - N 3. - P. 102-116.
10	10. A. Friedman, Differential Games, New York: Wiley, 1971, 350 p.
11	11. Hajek O. Control Theory in the Plane (Lecture Notes in Control and Information Sciences) - Berlin, New York: Springer-Verlag, 2009. - 220 p.
12	12. Hajek O. Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion. - NY.: Dove. Pub. 2008. - 288 p.
13	13. Isaacs R., Differential Games, J. Wiley, New York-London-Sydney, 1965, 384 p.
14	14. Ibragimov G.I. Collective pursuit with integral constrainson the controls of players, Siberian Advances inMathematics, 2004, v.14,No.2,p.13-26.
15	15. Ibragimov G.I. AbdRasid N., Kuchkarov A., Fudziah Ismail. Multi Pursuer Differential Game of Optimal Approach with Integral Constraints, Taiwanese Journal of Mathematics, 2015. - Vol. 19. - No 3. - P. 963-976.
16	16. Ibragimov G.I., Azamov A. A., Khakestari M. Solution of a linear pursuit-evasion game with integral constraints, ANZIAM Journal.Electronic Supplement.- 2010. - Vol.52. - P. E 59-E 75.
17	17. Imado F. Some practical approaches to pursuit-evasion dynamic games, CSA. - Elsevier, 2002. - Vol.38(2). - N 3. - P. 26-37.
18	18. Krasovskiy. A. N., Choi Y. S. Stochastic Control with the Leaders-Stabilizers. - Ekaterinburg : IMM Ural Branch of RAS,2001. - 51 p.
19	19. Krasovskii A. N., Krasovskii N. N. Control lunder Lack of Information. - Berlin etc. :Birkhauser, 1995. – 322, p.
20	20. Kuchkarov A.Sh. Solution of Simple Pursuit-Evasion Problem When Evader Moves on a Given Curve, International Game Theory Review. - World Scientific Publishing Company, 2010. - Vol.12. - N 3, p. 223-238.
21	21. Miller B., Rubinovich E.Y. Impulsive Control inContinuous and Discrete-Continuous Systems. - N.Y. : KluwerAcademic/Plenum Publishers, 2003. - 447 p.
22	22. Nahin P.J. Chases and Escapes: The Mathematics of Pursuit and Evasion. Princeton University Press, Princeton, 2012, - 260.
23	23. Petrosyan L. A. About some of the family differential gamesat a survival in the space Rn (in Russian), Dokl.Akad.Nauk SSSR, 1965, 161, No1, p.52-54.
24	24. Petrosyan L.A. The Differential Games of pursuit (in Russian), Leningrad, LSU, 1977, 224 p.
25	25. Petrosyan L.A., Rikhsiev B.B. Pursuit on the plane (in Russian), Nauka, Moscow, 1991, 96 p.
26	26. Petrosyan L.A., Mazalov V.V. Game Theory and Applications I, II, New York: Nova Sci. Publ., 1996, 211 p., 219 p.
27	27. Petrosyan L.A. Pursuit. Games with "a Survival Zone" (in Russian), Vestnic Leningard State Univ., 1967, No.13, p.76-85.
28	28. Petrosyan L.A., Dutkevich V.G. Games with "a Survival Zone", Occation L-catch (in Russian), Vestnic Leningrad State Univ.,1969, No.13, v.3, p.31-38.
29	29. Pontryagin L.S. "Linear Differential Pursuit Games" (in Russian), Math. Sb. [Math.USSR-Sb], 112, No.3, p.307-330.
30	30. Pshenichnyi B.N. The simple pursuit with some objects (in Russian), Cybernetics, 1976, No.3, pp.145-146.
31	31. Rikhsiev B.B. The differential games with simple motions (in Russian), Tashkent: Fan, 1989, 232 p.
32	32. Satimov N.Yu. Methods of solving of pursuit problem in differential games (in Russian), Tashkent: NUUz, 2003, 245 p.
33	33. Samatov B.T. The construction of the П-strategy for thegame on simple pursuit with integral constraints (in Russian). The boudary value problems for non-classical mathematical-physical equations. Tashkent: Fan, 1986, p. 402- 412.
34	34. Samatov B.T. The Differential Game with "A Survival Zone" with Different Classes of Admissiable Control Functions. Game Theory and Applications. Nova Science Publ. 2008.V.13.P.143-150.
35	35. Samatov B.T. The Game with "A Survival Zone" in the caseintegral-geometric constraints on the controls of the Pursuer, Uzb.Math.jornal - Tashkent, 2012. - No 7. - p. 64-72.
36	36. Samatov B.T. On a Pursuit-Evasion Problem under a Linear Change of the Pursuer Resource, Siberian Advances in Mathematics. –Allerton Press, Inc. Springer. - New York, 2013. - Vol. 23. - No 4. - P.294-302.
37	37. Samatov B.T. The Pursuit-Evasion Problem under Integral-Geometric constraints on Pursuer controls, Automation and Remote Control. - Pleiades Publishing, Ltd. - New York, 2013. -Vol. 74. - No 7. - P. 1072-1081.
38	38. Samatov B.T. The Resolving Functions Method for the Pursuit Problem with Integral Constraints on Controls, Journal of Automation and Information Sciences. - Begell House, Inc. (USA). 2013. - Vol. 45, No 8. - P.41-58.
39	39. Samatov B.T. The П-strategy in a differential game with linear control constraints, J. Appl. Maths and Mechs. - Elsevier. - Netherlands,2014. - Vol. 78. - No 3. - P. 258-263.
40	40. Samatov B.T. Problems of group pursuit with integral constraints on controls of the player. I, Cybernetics and Systems Analysis.–Springer International Publishing AG. - Switzerland, 2013. - Vol.49. - No5. - P.756-767.
41	41. Samatov B.T. Problems of group pursuit withintegral constraints on controls of the player. II, Cybernetics andSystems Analysis.–Springer International Publishing AG -Switzerland, 2013. - Vol. 49. - No 6. - P.907-924.