414

Ushbu maqolada differensial o‘yinlar nazariyasida Gronuoll  
tipidagi  tengsizliklarni  qo‘llanishi  ko‘rilgan.  Bunda  o‘yinchilarning  boshqaruv  funksiyalari, 
geometrik chegaralanishlarni umumlashtiruvchi Gronuoll tipidagi chegaralanishlar uchun chiziqli 
differensial  o‘yinlarda  qochish masalasi  o‘rganiladi.   Bu  yerda  qochish masalasini  yechish  uchun 
qochuvchiga  alohida  strategiya  taklif  etiladi  va  o‘yinchilar  orasidagi  masofani  aniqlovchi 
funksiyaning  xossalari  o‘rganiladi.  Maqolada  Ayzeks,  Petrosyan,  Pshenichniy  va  boshqa 
tadqiqotchilar,  shuningdek mualliflarning avvalgi  ishlari  rivojlantiriladi va kengaytiriladi. Bunda 
qochish masalasini yechish uchun yangi yetarlilik shartlari taklif etiladi.

  • Internet ҳавола
  • DOI
  • UzSCI тизимида яратилган сана 25-01-2021
  • Ўқишлар сони 406
  • Нашр санаси 25-01-2021
  • Мақола тилиO'zbek
  • Саҳифалар сони26-33
Ўзбек

Ushbu maqolada differensial o‘yinlar nazariyasida Gronuoll  
tipidagi  tengsizliklarni  qo‘llanishi  ko‘rilgan.  Bunda  o‘yinchilarning  boshqaruv  funksiyalari, 
geometrik chegaralanishlarni umumlashtiruvchi Gronuoll tipidagi chegaralanishlar uchun chiziqli 
differensial  o‘yinlarda  qochish masalasi  o‘rganiladi.   Bu  yerda  qochish masalasini  yechish  uchun 
qochuvchiga  alohida  strategiya  taklif  etiladi  va  o‘yinchilar  orasidagi  masofani  aniqlovchi 
funksiyaning  xossalari  o‘rganiladi.  Maqolada  Ayzeks,  Petrosyan,  Pshenichniy  va  boshqa 
tadqiqotchilar,  shuningdek mualliflarning avvalgi  ishlari  rivojlantiriladi va kengaytiriladi. Bunda 
qochish masalasini yechish uchun yangi yetarlilik shartlari taklif etiladi.

Русский

 Основная цель настоящей работы является применение  
неравенства  Грануолла  в  теории  дифференциальных  игр.  Здесь  рассматривается  задача 
убегания  для линейных дифференциальных игр с ограничением типа Грануолла, которое в 
некотором  смысле  обобщает  геометрическое  ограничение  на  управления  игроков.  Для 
решения  задачи   предлагается   специальная стратегия для убегающего игрока и изучается 
функция  определяющая  расстояния между  игроками.  В  настоящей  статье  развиваются 
идеи предложенные в работах Айзекса, Петросяна, Пшеничного и других, а так же авторов. 
Здесь получены новые достаточные условия разрешимости задачи убегания. 

English

The main aim  of  this work  is  to present  some natural applications of Gronwall 
type inequalities in the Differential Games. In the present, the evasion problem is studied in linear 
differential  games when Gronwall  type  constraints  imposed  on  control  functions  of  players. The 
Gronwall  type  constraint  generalizes  geometrical  constraint.  To  solve  the  evasion  problem,  we 
propose a particular strategy for evader and study its structure depending on the parameters. This 
work  develops  and  extends  the  ideas  of  works  of  Isaacs,  Petrosyan,  Pshenichnii  and  other 
researchers,  including  the author. Here  the new sufficient solvability conditions  for evader will be 
proposed.

№ Муаллифнинг исми Лавозими Ташкилот номи
1 Samatov B.T.
2 Soyibboev U.B.
3 Akbarov A.K.
№ Ҳавола номи
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