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Nonlinear dynamical systems of trajectory design for 3D horizontal well and their optimal controls. (English) Zbl 1129.37045

Summary: The trajectory design of horizontal well is a optimal control problem of nonlinear multistage dynamical systems. It is often sought using trial-and-error methods, but these methods depend on the experience of designers and workers. In this paper, we create a new optimal control model of nonlinear dynamical systems for the trajectory design of horizontal wells. Several properties are discussed. A uniform design method is used to choose the initial points in the feasible region. We demonstrate how to decompose the feasible region into finite subregions in which the improved Hook-Jeeves algorithm is employed to search optimal solution. Finally, the feasible optimization algorithm is constructed to find the optimal solution of the system. Several results show the validity of our algorithm. This is preferable, since our method is independent of the experience.

MSC:

37M05 Simulation of dynamical systems
90C90 Applications of mathematical programming
93C10 Nonlinear systems in control theory
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References:

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