This study explores optimal control in the case when certain input uncertainties cannot be well quantified. In these scenarios, the decision-maker prefers to have the most flexibility, which is defined to be the largest range of options for decision variables, and still achieve the objectives of the operation while satisfying all constraints. Each decision variable is generalized to be a range of potential actions. These ranges are modelled with random variables, thus uncertainty quantification techniques are employed to compute expected values of objectives and probabilities of chance constraints. The proposed framework determines optimal probability densities for the decision variables by treating the amount of flexibility as an additional objective. There is a clear trade-off between the amount of flexibility that can be allowed and the resulting expected values of the other objectives. A dimension reduction technique is employed to ensure a reasonable dimension for the search space.

本研究探讨了某些输入不确定性无法很好量化的情况下的最佳控制。在这些场景中，决策者更愿意拥有最大的灵活性，即定义为决策变量的选择范围最大，在满足所有约束条件的同时仍能实现操作目标。每个决策变量都被概括为一系列潜在的行动。这些范围是用随机变量建模的，因此使用不确定性量化技术来计算目标的预期值和机会约束的概率。所提出的框架通过将灵活性量作为附加目标来确定决策变量的最佳概率密度。在可以允许的灵活性和其他目标的预期值之间存在明显的权衡。采用降维技术来确保搜索空间的合理维数。