Değişken gecikmeli kısıtlı stokastik kontrol geçiş sistemleri için regülatör problemi

Bu makalede, doğrusal stokastik denklemler sınıfıyla ifade olunan geçiş sistemleri ele alınmıştır. Gecikmeli faz vekontrol parametreleri içeren diferansiyel denklemler için karesel amaç fonksiyonu olan optimal kontrol problemioluşturulmuş ve sağ uç noktasında kısıta sahip olan durum için optimizasyon problemi incelenmiştir. LiteratürdeDoğrusal Karesel Regülatör olarak bilinen ve sabit katsayılı stokastik diferansiyel denklemlerle ifade olunan buproblemin optimal lığı için yeter ve gerek koşul, maksimum prensibi şeklinde ispatlanmıştır. Bunun yanı sıra geçişsistemleri için önemli olan geçiş noktalarının bulunması için karşıtlık koşulları bulunmuştur. Sonda ise DoğrusalKaresel Regülatör problemleri için önem taşıyan optmal kontrolün geri dönüşüm şekli bulunmuştur. Çözümü,Riccati denklemleriyle ifade olunan geri dönüşüm problemi, bu çalışmada değişken gecikmeli stokastik sistemleriçin uygulanmıştır.

Regulator problem of restricted stochastic switching systems with variable delay

In this paper, the switching systems expressed by the class of linear stochastic differential equations are discussed. For the differential equations containing the delayed phase and delayed control parameters, the optimal control problem with the quadratic cost function is constructed. Stochastic optimization problem is examined for the systems with the the right end point restriction. Linear Quadrature Regulator problem expressed by the stochastic differential equations is investigated. Necessary and sufficient condition in terms of maximum principle has been proven. In addition, transversation conditions have been found to establish the transition points that are important for the switching systems. It is well known that, the feedback form of optimal control important for the Linear Quadrature Regulator problems. The solution of feedback problem directly relate with Riccati equations. Mentioned problem is solved for the stochastic differential equation with variable delay.

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