论文标题
解决机会限制的最佳控制问题的温暖开始方法
A Warm Start Method for Solving Chance Constrained Optimal Control Problems
论文作者
论文摘要
开发了一种温暖的开始方法，以有效地解决复杂的机会约束最佳控制问题。温暖的开始方法解决了使用有偏见的内核密度估计器和Legendre-Gauss-Radau colotation以$ HP $自适应网状细化方法解决机会限制最佳控制问题的计算挑战。为了应对计算挑战，温暖的开始方法既可以提高机会约束最佳控制问题的起点，也可以通过网状细化迭代来骑自行车的效率。改进是通过调整内核密度估计器的参数以及作为解决方案过程的一部分实现内核开关来实现的。另外，通过一系列网状细化迭代，将偏置核密度估计器的样品数量逐渐增加。因此，温暖的开始方法是调整参数，内核开关和样本量增量增加的组合。这种温暖的开始方法成功地应用了使用有偏见的内核密度估计器和legendre-gauss-radau搭配以计算有效的方式解决两个具有挑战性的最佳控制问题。
A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre-Gauss-Radau collocation.
