Runge-Kutta scheme for stochastic optimal control problems

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2017

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Öz Bakan, Hacer

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In this thesis, we analyze Runge-Kutta scheme for the numerical solutions of stochastic optimal control problems by using discretize-then-optimize approach. Firstly, we dis- cretize the cost functional and the state equation with the help of Runge-Kutta schemes. Then, we state the discrete Lagrangian and take the partial derivative of it with respect to its variables to get the discrete optimality system. By comparing the continuous and discrete optimality conditions, we ﬁnd a relationship between the Runge-Kutta coef- ﬁcients of the state and adjoint equation, so that we present Runge-Kutta scheme for the adjoint pair (p(t),q(t)). Similar to the deterministic setting, the issue of conver- gence is important when dealing with a numerical scheme. In stochastic case, this can be achieved either by using the strong-order convergence or weak-order convergence criteria. We match the stochastic Taylor expansion on the exact solution of continuous optimality system with the stochastic Taylor expansion of approximate solution of our discrete optimality system, term by term, in order to get both strong and weak-order conditions. The thesis ends with a conclusion and a future outlook to forthcoming research and application.

Subject Keywords

Runge-Kutta formulas., Stochastic differential equations., Stochastic partial differential equations., Stochastic differential equations

URI

http://etd.lib.metu.edu.tr/upload/12621378/index.pdf
https://hdl.handle.net/11511/26953

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

H. Öz Bakan, “Runge-Kutta scheme for stochastic optimal control problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.