SODDA HARAKATLI KO‘P O‘YINCHILI QUVISH-QOCHISH DIFFERENSIAL O‘YINLARIDA SINGULAR SIRTLAR VA TO‘LIQ YECHIMLAR
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Abstract
Ushbu maqolada Isaacsning sodda harakat modeli asosida tekislikdagi ko‘p o‘yinchili quvish-qochish differensial o‘yinlari uchun to‘liq yechimlar qurilishi ko‘rib chiqiladi. Asosiy e’tibor ikki quvuvchi va bir qochuvchi (2P1E) hamda uch quvuvchi va bir qochuvchi (3P1E) o‘yinlariga qaratilgan bo‘lib, quvuvchilarning tezliklari teng yoki qochuvchinikidan yuqori deb olinadi. Asosiy hissa — optimal trayektoriyalar kesishganda paydo bo‘ladigan singular sirtlarni (dispersal sirtlar, universal sirtlar va to‘siq sirtlar) qat’iy tavsiflashdan iborat. Hamilton–Jacobi–Isaacs (HJI) tenglamasi uchun xarakteristikalar usuli va Apolloniy doiralari asosidagi geometrik konstruksiyalardan foydalanib, butun fazo holati bo‘yicha qiymat funksiyasining aniq ifodalari olingan. Olingan teskari bog‘lanish strategiyalarining optimalligini isbotlovchi teoremalar qiymat funksiyasining HJI tenglamasining viscosity yechimi ekanligini va tegishli chegaraviy shartlarni qanoatlantirishini tekshirish orqali isbotlangan. Raqamli misollar analitik natijalarni tasdiqlaydi. Ushbu yondashuv o‘yinchilar sonini oshirish va murakkabroq kinematikalarga o‘tish uchun asos yaratadi.
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