Tezin ikinci b¨ol¨um¨unde, anahtarlamalı sistemler ic¸in lineer kuadratik opti-mal kontrol problemi ele alınmıs¸tır. Problem; bilinmeyen anahtarlama parametre-sine ba˘glı ve sabit aralıkta bilinmeyen sınır de˘gerlere sahip integrale d¨ons¸t¨ur¨ulerek sonlu boyutlu bir optimizasyon problemine indirgenmis¸tir. Kontrol probleminin c¸¨oz¨um¨unde Gradyan Projeksiyon Metodu kullanılarak optimal anahtarlama anı, op-timal kontrol fonksiyonu ve opop-timal maliyet de˘geri bulunmus¸tur. Her bir opop-timal arg¨uman uygun aralıklarda grafikler ¨uzerinde g¨osterilmis¸tir.
Uc¸¨unc¨u b¨ol¨umde, sıc¸rama-sistemli orta-alan stokastik diferansiyel denklem-¨ leri ic¸in optimal s¨urekli-sing¨uler kontrol¨un gereklilik kos¸ulları elde edildi. Kontrol probleminin analizinde maksimum prensip yaklas¸ımı ile karma konveks-spike per-turbasyon y¨ontemi kullanıldı ve elde edilen souc¸lar Markowitz ’in ortalama-varyans portfoly¨o sec¸im problemine uygulandı.
D¨ord¨unc¨u b¨ol¨umde, Levy proseslerine ba˘glı Teugels martingaller tarafından idare olunan orta-alan ileri-geri stokastik diferansiyel denklemleri ic¸in maksimum prensip formundaki optimalli˘gin gereklilik ve yeterlilik kos¸ulları elde edilmis¸tir.
Kontrol probleminin analizinde konveks varyasyon metodu ve dualite ilis¸kisi kullanılmıs¸tır. Elde edilen souc¸uc¸lar Markowitz’ in ortalama-varyans porfoly¨o sec¸im problemine uygulanmıs¸tır.
Son b¨ol¨umde, genel kontroll¨u lineer olmayan McKean-Vlasov tipi stokastik diferansiyel denklemlerin idare etti˘gi sistemlerde optimal stokastik sing¨uler kontrol problemi ic¸in gereklilik ve yeterlilik kos¸ulları elde edildi. Kontrol probleminin analizinde konveks perturbasyon metodu kullanıldı ve ulas¸ılan teorik sonuc¸lar
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