SavedAdd your journal

Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :B-Teorik Bilimler / 2016 / Cilt: 4 - Sayı: 2

GECİKMELİSTOKASTİK GEÇİŞ SİSTEMLERİİÇİN DOĞRUSAL KUADRATİK KONTROLPROBLEMİ

LINEAR QUADRATIC CONTROLPROBLEM OF STOCHASTIC SWITCHINGSYSTEMS WITH DELAY

Charkaz Arif AGHAYEVA
Pages
52–58
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A necessary and sufficient condition of optimality for stochastic linear switching systems with delay is obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Linear Quadratic (LQ) problems constitute important class of optimal control problems.
📊
Key Findings & Data:The solution of this problem has had a profound impact on many economics, engineering, chemical applications and many nonlinear control problems can be approximated by the LQ problems.
💡
Conclusion & Impact:A necessary and sufficient condition of optimality for stochastic linear switching systems with delay is obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Linear Quadratic (LQ) problems constitute important class of optimal control problems. The solution of this problem has had a profound impact on many economics, engineering, chemical applications and many nonlinear control problems can be approximated by the LQ problems. The contribution of this paper is to investigate the stochastic optimal control problem of linear switching systems with quadratic cost functional. A necessary and sufficient condition of optimality for stochastic linear switching systems with delay is obtained.

Özet

Doğrusal Kuadratik (DK) problem optimal control problemlerinin mühüm bir sınfını oluşturuyor. Bu problemin çözümünün birçok ekonomi, mühendislik, kimya uygulamalına önemli etkisi var. Aynı zamanda çok sayıda doğrusal olmayan kontrol problemleri DK problemleriyle yakınsanabilir. Bu çalışmada kuadratik amaç fonksiyonu olan doğrusal geçiş sistemleri için stokastik optimal problemi incelenmiştir. Gecikmeli stokastik doğrusal geçiş sistemlerinin optimal çozümü için gerekli ve yeterli koşullar bulunmuştur.

🔖

Cite This Article

AGHAYEVA, C. A. (2022). GECİKMELİSTOKASTİK GEÇİŞ SİSTEMLERİİÇİN DOĞRUSAL KUADRATİK KONTROLPROBLEMİ. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :B-Teorik Bilimler, Cilt: 4 - Sayı: 2, 52–58. https://ajindex.com/articles/438562

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. Gikhman I, Skorokhod A. Stochastic Differential Equations. Germany, Berlin: Springer, 1972. Mao X. Stochastic Differential Equations and Their Applications. Chichester: Horwood Publication House, 1997. Chojnowska-Michalik A. Representation theorem for general stochastic delay equations. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 1978;7: 635-642.
  2. Kolmanovsky V, Myshkis, A. Applied Theory of Functional Differential Equations., Dordrecht: Kluwer Academic Publishers, 1992.
  3. Agayeva C, Allahverdiyeva J. On one stochastic optimal control problem with variable delays, Theory of stochastic processes, Kiev 2007; 13: 3-11.
  4. Chernousko F, Ananievski, I. Reshmin, S. Control of Nonlinear Dynamical Systems: Methods and Applications (Communication and Control Engineering). Germany,Berlin: Springer, 2008. Elsanosi I, Øksendal B, Sulem A. Some solvable stochastic control problems with delay. Stoch. Stoch. Rep. 2000; 1-2: 69-89.
  5. Federico S, Golds B, Gozzi F. HJB equations for the optimal control of differential equations with delays and state constraints, II: optimal feedbacks and approximations. SIAM J. Control Optim.;49:2378-2414.
  6. Fleming W, Rishel R. Deterministic and Stochastic Optimal Control. New York, USA: Springer, Larssen B. Dynamic programming in stochastic control of systems with delay. Stoch. Stoch. Rep.; 3-4: 651-673. Kalman R. Contributions to the theory of optimal control, Bol. Soc. Math. Mexicana, 1960; 5:102- Anderson B, Ilchmann A, Wirth F. Stabilizability of time-varying linear systems. Systems and Control Letters, 2013; 62: 747-755.
  7. Bensoussan A, Delfour M, Mitter S. The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon; survey and examples. In: IEEE Conference on Decision and Control; December 1976;
  8. Clearwater, Fla, USA: pp.746-751. Balakrishnan A. A note on the structure of optimal stochastic control, Applied Mathematics and Optimization, 1975; 1: 87 -94. Hoek J, Elliott R. American option prices in a Markov chain model, Applied Stochastic Models in Business and Industry, 2012; 28: 35-39.
  9. Kohlmann M, Zhou X. Relationship between backward stochastic differential equations and stochastic controls: A linear-quadratic approach, SIAM,Journal on Control and Optimization, 2000;:1392-1407. Wonham W. On a matrix Riccati equation of stochastic control, SIAM,Journal on Control and Optimization, 1968; 6: 312-326. Bellman R. Functional equations in the theory of dynamic programming, positivityand qu