Three-dimensional trajectory design for horizontal well based on optimal switching algorithms.
This paper considers a three-dimensional trajectory design problem for horizontal well. The problem is formulated as an optimal control problem of switched systems with continuous state inequality constraints. Since the complexity of such constraints and the switching instants is unknown, it is difficult to solve the problem by standard optimization techniques. To overcome the difficulty, by a time-scaling transformation, a smoothing technique and a penalty function method, an efficient computational method is proposed for solving this problem. Convergence results show that, for a sufficiently large penalty parameter, any local optimal solution of the approximate problem is also a local optimal solution of the original problem. Two numerical examples are presented to illustrate the efficiency of the approach proposed.
School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, PR China. Electronic address: seuwuxiang@163.com.
Xiang
X
Wu
School of Automation, Southeast University, Nanjing 210096, PR China; Key Laboratory of Measurement and Control of CSE, Ministry of Education, Southeast University, Nanjing 210096, PR China. Electronic address: kjzhang@seu.edu.cn.
Kanjian
K
Zhang
Horizontal well trajectory design; Optimal control; Penalty function method; Smoothing technique; Time-scaling transformation