论文标题
使用偏置核密度估计器的机会限制的最佳控制方法
Method for Chance Constrained Optimal Control Using Biased Kernel Density Estimators
论文作者
论文摘要
开发了一种方法来求解机会约束的最佳控制问题。机会限制被重新重新构成为非线性约束，保留了原始约束的概率属性。重新制定将限制的最佳控制问题转化为可以通过数值解决的确定性最佳控制问题。本文开发的新方法使用Markov链蒙特卡洛（MCMC）采样和内核密度估计器的概率约束近似，其内核具有绑定指示器函数的积分函数。由内核密度估计器应用而产生的非线性约束的设计界限不违反原始机会约束的界限。该方法是根据软性月球着陆最佳控制问题的非平凡机会约束修改进行测试的，并将结果与使用保守的最佳控制问题确定性公式获得的结果进行了比较。结果表明，这种新方法有效地解决了频率受限的最佳控制问题。
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo (MCMC) sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a non-trivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. The results show that this new method efficiently solves chance constrained optimal control problems.
