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Değişken gecikmeli kısıtlı stokastik kontrol geçiş sistemleri için regülatör problemi

Yıl 2020, , 997 - 1005, 26.09.2020
https://doi.org/10.17798/bitlisfen.633210

Öz

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

Kaynakça

  • Kolmanovsky V., Myshkis A. 1992. Applied Theory of Functional Differential Equations. Dordrecht: Kluwer Academic Publishers.
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  • Chernousko F., Ananievski I., Reshmin S. 2008. Control of Nonlinear Dynamical Systems: Methods and Applications (Communication and Control Engineering). Germany,Berlin: Springer.
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  • Kalman R., 1960. Contributions to the theory of optimal control. Boletin De La Sociedad Matematica Mexicana, 5:102–119. Bellman R. 1955. Functional equations in the theory of dynamic programming, positivity and quasilinearity. Proceeding of National Academy of Science, USA, 41:743–746.
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  • Delfour M.C. 1986. The linear quadratic optimal control problem with delays in state and control variables: a state space approach. SIAM J Control Optim. 24:835-883.
  • Ichikawa A. 1982. Quadratic control of evolution equations with delays in control. SIAM, Journal on Control and Optimization, 20:645-668.
  • Bismut J. M. 1976. Linear quadratic optimal stochastic control with random coefficients, SIAM , Journal on Control and Optimization, 14:419–444.
  • Wonham W. 1968. On a matrix Riccati equation of stochastic control, SIAM ,Journal on Control and Optimization; 6: 312–326.
  • Boukas E.-K. 2006. Stochastic Switching Systems. Analysis and Design. Boston, USA:Birkhauer.
  • Kharatatishvili G., Tadumadze T. 1997. The problem of optimal control for nonlinear systems with variable structure, delays and piecewise continuous prehistory. Memoirs on Differential Equations and Mathematical Physics, 11: 67-88.
  • Tadumadze T., Arsenashvili A. 2008. Optimization of a delay variable structure system with mixed intermediate condition. Bulletin of the Georgian National Academy of Sciences , 2(3):22–26.
  • Aghayeva Ch. 2014. Necessary condition of optimality for stochastic switching systems with delay. In: International Conference on Mathematical Models and Methods in Applied Sciences; 23-25 September 2014; Saint Petersburg, Russia: MMAS’14. pp. 54-58.
  • Abushov Q., Aghayeva Ch. 2014. Stochastic maximum principle for the nonlinear optimal control problem of switching systems, Journal of Computational and Applied Mathematics, 259: 371-376.
  • Agayeva Ch. 2016. Linear Quadratic Control Problem of Stochastic Switching Systems with Delay, Anadolu University Journal of Science and Technology-B, Theoretical Sciences, 4(2), pp.52-58.
  • Ağayeva Ç., Takan A.M. 2018. Restricted Optimal Control Problem for Stochastic Switching Systems with Variable Delay, Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, 6(2), s. 565-569.
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  • Bellman R. 1955. lFunctional equations in the theory of dynamic programming, positivity and quasilinearity. Proceeding of National Academy of Science, USA, 41:743–746.
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makalesi
Yazarlar

Çerkez Ağayeva 0000-0003-0507-9785

Yayımlanma Tarihi 26 Eylül 2020
Gönderilme Tarihi 15 Ekim 2019
Kabul Tarihi 16 Haziran 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

IEEE Ç. Ağayeva, “Değişken gecikmeli kısıtlı stokastik kontrol geçiş sistemleri için regülatör problemi”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 9, sy. 3, ss. 997–1005, 2020, doi: 10.17798/bitlisfen.633210.



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