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


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

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

  • Cilt numarası: 157
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.apnum.2020.07.002
  • Dergi Adı: APPLIED NUMERICAL MATHEMATICS
  • Sayfa Sayıları: ss.470-489

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.