Stochastic optimal control and algorithm of the trajectory of horizontal wells

Authors:
An Li;Enmin Feng;Xuelian Sun
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 2
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Directional derivatives of the solution of a parametric nonlinear program

Mathematical Programming: Series A and B
Multi-objectives fuzzy models for desingning 3D trajectory in horizontal wells

The Korean Journal of Computational & Applied Mathematics

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Abstract

This paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke-Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm.