Kirish…………………………………………………………………………4I bob.Uzluksiz dinamiktizimlarda optimal boshqaruv masalasi uchun maksimum prinsipi……………………………………… 81-§Pontryaginning maksimum prinsipi-optimallikning zaruriy sharti………………………………………………………………. 81.1Optimal boshqaruv masalasining qo‘yilishi……………………….81.2Pontryaginning maksimum prinsipi………………………………..111.3Maksimumprinsipining chegaraviy masalasi……………………..142-§Terminal boshqaruv masalasi……………………………………...192.1Terminal boshqaruv masalasida maksimum prinsipi……………...192.2Ekstremal boshqaruvlar…………………………………………...212.3Chiziqli terminal boshqaruv masalasi……………………………..243-§Chiziqli boshqaruv tizimlari uchun tezkormasala………………...263.1Chiziqli boshqaruv tizimi. Ekstremal prinsip……………………...263.2Chiziqli tezkor masalada optimallikning zaruriy va yetarli shartlari……………………………………………………………. 293.3Tez harakat masalasi uchun Pontryaginning maksimum prinsipi…313.4Chiziqli stasionar tezkor masala…………………………………...324-§Tezkorlik masalasida ajratuvchi giperteksliklar usuli……………..364.1Chiziqli tezkorlik haqidagi masalaning geometrik tavsifi…………364.2.Ko'p qadamlialgoritim…………………………………………….375-§.Qavariq faza cheklashlarga ega tezkorlik masalasi………………..435.1.Masalaning qo'yilishi va uning funksional fazoda ifodalanishi……435.2.Masalani yechishning umumiy sxemasi..…………………………455.3.Erishiladigan to'plam qavariqligi…………………………………..465.4.Berilgan normalli tayanch tekslikni qurish………………………...465.5.Ajratuvchi gipertekslik normali yo'nalishini tanlash………………485.6.Algoritim…………………………………………………………..51II bob.Isitishjarayonlarini optimal boshqaruv masalasi……………..541-§Isitish jarayonlarining matematik modeli………………………….542.1Muhitda issiqlik tarqalish differensial tenglamasi…………………542.2Parabolik tipli tenglamalarga qo’yilgan chegaraviy masalalarni yechishning Fur’e usuli…………………………………………... 582-§Issiqlik o’tkazuvchanlikni boshqaruv masalasida faza cheklanishlari qatnashmagan hol…………………………………. 612.1Plastinkani tashqi issiqlik manbalari bilan qizdirish………………622.2Plastinkani qizdirish jarayoni matematik modeliuchun to'g'ri65