School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, PR China.
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.
ISA Trans. 2015 Sep;58:348-56. doi: 10.1016/j.isatra.2015.04.002. Epub 2015 Apr 24.
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.
本文考虑了水平井的三维轨迹设计问题。该问题被表述为具有连续状态不等式约束的切换系统的最优控制问题。由于这种约束和切换时刻的复杂性未知，因此很难通过标准优化技术来解决这个问题。为了克服这个困难，通过时间尺度变换、平滑技术和罚函数方法，提出了一种有效的计算方法来解决这个问题。收敛结果表明，对于一个足够大的罚参数，近似问题的任何局部最优解也是原问题的局部最优解。通过两个数值例子说明了所提出方法的有效性。
