Optimal Control And Algorithm Of The Trajectory Of Horizontal Well With Perturbation

This dissertation, based on practical background of designing the 3D-trajectory of horizontal well, establishes a multi-phase, nonlinear, stochastic dynamic system of the trajectory of horizontal well, taking perturbations in the engineering as stochastic process, with inclination, azimuth, north coordinate,east coordinate, vertical -depth coordinate as state variables, and tool-face angle, curvature radius, curve length as control variables. There are two aims for designing the 3D-trajectory of horizontal well. Firstly, the terminal output of this dynamical system will best approximate the corresponding values of the target point. Secondly, the total length of 3D-trajectory of horizontal well will be as short as possible. Based on the stochastic dynamic system, taking the aims mentioned above as the performance index, a stochastic optimal control of the trajectory of horizontal well is established. The present dissertation intends to study the nonlinear, multi-phase, stochastic optimal control system, construct a global optimization algorithm, and applies the algorithm into the practical design of the trajectory of horizontal well.Chapter 1 reviews the progress of control theory, and introduces many achievements by scholars home and aboard hi the field of the designing the trajectory of horizontal well. Chapter 2 mainly discusses some basic knowledge, including some conceptions and properties of stochastic dynamic system and its optimal algorithm which serves as the preparation of the proceeding research. Chapter 3 and Chapter 4 present the main study results from this dissertation, which can be summarized as follows:1. For the nonlinear, multi-phase, stochastic optimal control system, the unique existence of the solution of the state equations and the existence of optimal solutions of the optimal control system are discussed, and the necessary condition of the optimality is gained via dynamic programming principle.2. In order to obtain the global optimal solution of the nonlinear, multi-phase, stochastic optimal control system, the stochastic optimal control system is transformed into a nonlinear stochastic programming. We discuss here that a local solution depends in a continuous way on the parameter (perturbation).3. Utilizing the properties a revised Hooke-Jeeves algorithm is proposed and worked out by C language. The numerical results illustrate the validity and efficiency of algorithm.