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In theory of differential games, the problems put geometric, integral and their 
being together constraints to controls were studied sufficiently. In this paper, the evasion problem 
of the second order differential game will be stuided  in which case new control classes with the 
name of constraint of Gronwall type have been introduced to control functions. 

  • Web Address
  • DOI
  • Date of creation in the UzSCI system 04-03-2020
  • Read count 442
  • Date of publication 10-07-2019
  • Main LanguageIngliz
  • Pages3-9
English

In theory of differential games, the problems put geometric, integral and their 
being together constraints to controls were studied sufficiently. In this paper, the evasion problem 
of the second order differential game will be stuided  in which case new control classes with the 
name of constraint of Gronwall type have been introduced to control functions. 

Ўзбек

Differensial  o‘yinlar nazariyasida  boshqaruvlarga  geometrik,  integral  va 
ularning  birgalikdagi  chegaralanishlari  qo‘yilgan  masalalar  yetarlicha  o‘rganilgan.  Ushbu 
maqolada boshqaruv funksiyalariga Gronuoll tipidagi chegaralanish nomi bilan yangi boshqaruv 
sinflari kiritilgan holda ikkinchi tartibli differensial o‘yinning qochish masalasi o‘rganilgan.  

Русский

В  теории  дифференциальных  играх  достаточно  изучены  задачи 
задающего  при  управления  геометрического,  интегрального  и  их  совместных 
ограничениях.  В  работе  изучается  задача  убегания  для  дифференциальных  игр  второго 
порядка, когда начальные состояния и начальные скорости игроков линейно зависимы при 
ограничениях Гронуолла на управления.  

№ Author name position Name of organisation
1 Horilov M.A. NamSU
2 Soyibboev U.B. NamSU
3 Hamitov A.A. NamSU
№ Name of reference
1 Gronwall T.H. (1919) Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. 20(2):293–296.
2 Azamov A.A., Samatov B.T.(2010) The Π-Strategy: Analogies and Applications. The Fourth International Conference Game Theory and Management, St. Petersburg: 33 – 47.
3 Subbotin A.I., Chentsov A.G. (1981). Optimization of Guaranteed Result in Control Problems. Nauka, Moscow.
4 Jack K. Hale. (1980). Ordinary differential equations. Krieger Malabar, Florida: 28 – 37.
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