Lineer Olmayan Bazı Noktasal İzlemeli Kontrol Problemleri Ve Çözüm Yöntemleri
Lineer Olmayan Bazı Noktasal İzlemeli Kontrol Problemleri Ve Çözüm Yöntemleri
Dosyalar
Tarih
Yazarlar
Kızılsaç, Bayram Barış
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science And Technology
Institute of Science And Technology
Özet
Bu çalışmada lineer olmayan diferansiyel denklemler ile ifade edilebilen bazı noktasal izlemeli kontrol problemleri incelenmiştir. Problemin bazı durumlarda kesin çözümünün bulunabildiği, çoğu uygulamada çözümün yaklaşık olarak bulunmasının önem kazanacağı belirtilmiştir. Çözümü kesin olarak bulunabilen bazı noktasal izlemeli kontrol problemleri ele alınarak, farklı yöntemlerle bulunan kesin çözümleri verilmiştir. Yaklaşık çözümü elde etmek için bir ardışık izlemeli kontrol algoritması tanıtılmıştır. Tanıtılan algoritma açık ve kapalı kontrol düzenleyicileri olmak üzere iki şekilde incelenmiştir. Son olarak noktasal izlemeli kontrol problemi penaltı yöntemi kullanılarak incelenmiştir. Bu yöntem ile noktasal izlemeli kontrol problemi belirli bir optimal kontrol problemine indirgenmiştir. Daha sonra Pontryagin’ in maksimum ilkesi uygulanarak noktasal izlemeli kontrol probleminin genelleşmiş çözümü olarak adlandırılan kontrolün gerekli koşulları bulunmuştur.
This work investigates some of the pointwise learning control problems governed by nonlinear ordinary differantial equations. It is stressed that, only for some of the problems, the exact analytical solutions can be found, but for the most others, methods to obtain a reliable approximate solution is important. Rewieving some of the exactly soluable problems, various methods for finding the exact solution are discussed. For obtaining the approximate solutions to the pointwise learning control problems an iterative learning control algorithm is presented. The designed algorithm is developed in two forms, for both the off-line and the on-line types of the control regulators. Then the pointwise learning control problem is investigated by utilizing the penalty mathod. By this, the pointwise learning control problem is reduced to a definite optimal control problem. Then applying the maximum principle of Pontryagin, the necesarry conditions of the control, named as the generalized solution of the pointwise learning control problem, is obtained.
This work investigates some of the pointwise learning control problems governed by nonlinear ordinary differantial equations. It is stressed that, only for some of the problems, the exact analytical solutions can be found, but for the most others, methods to obtain a reliable approximate solution is important. Rewieving some of the exactly soluable problems, various methods for finding the exact solution are discussed. For obtaining the approximate solutions to the pointwise learning control problems an iterative learning control algorithm is presented. The designed algorithm is developed in two forms, for both the off-line and the on-line types of the control regulators. Then the pointwise learning control problem is investigated by utilizing the penalty mathod. By this, the pointwise learning control problem is reduced to a definite optimal control problem. Then applying the maximum principle of Pontryagin, the necesarry conditions of the control, named as the generalized solution of the pointwise learning control problem, is obtained.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2001
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2001
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2001
Anahtar kelimeler
Noktasal İzlemeli Kontrol,
Ardışık İzlemeli Kontrol,
Pointwise Learning Control,
Iterative Learning Control