Strong-order conditions of Runge-Kutta method for stochastic optimal control problems

Yilmaz F. N., Bakan H. O., Weber G.

APPLIED NUMERICAL MATHEMATICS, cilt.157, ss.470-489, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 157
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.apnum.2020.07.002
  • Dergi Adı: APPLIED NUMERICAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.470-489
  • Anahtar Kelimeler: Optimal control, Stochastic differential equations, Runge-Kutta method, Stratonovich-Taylor expansion, APPROXIMATION
  • Gazi Üniversitesi Adresli: Evet

Özet

In this work, we obtain strong-order conditions of the Runge-Kutta method for the optimal control of the stochastic differential equations. We follow the discretize then optimize approach in order to get the optimality system. We compare Stratonovich-Taylor expansions of the exact solution and approximation method of the stochastic optimal control problem defined by the Runge-Kutta scheme successively to get the strong-order conditions. We derive the strong order-1.5 conditions and verify by a numerical example. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.