不确定性下基于场景的动态优化的统计推断
Statistical Inference for Scenario-Based Dynamic Optimization under Uncertainty
- Sandia National Laboratories（桑迪亚国家实验室）
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院 H. 米尔顿·斯图尔特工业与系统工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究不确定参数下有限时域开环动态优化问题，通过用采样参数平均值代替预期性能准则，基于稳定性估计得出统计理论，得到总体最优值置信区间，方法在补料分批案例中得以验证。
AI中文摘要：
受间歇和半间歇过程操作的启发，我们研究具有不确定参数的有限时域开环动态优化问题。一种常见的计算方法是用有限多个采样参数实现的平均值代替预期性能准则。我们为所得基于样本的最优值作为总体最优值的估计器发展了一种统计理论。分析基于一个稳定性估计，该估计表明终端损失在时间积分控制上Lipschitz连续依赖，时间积分控制记录了截至每次的累积输入。此估计为基于样本的目标产生一个泛函中心极限定理以及为相应的最优值误差产生一个统计极限定理。结果，我们得到了总体最优值的置信区间。当总体优化器唯一时，极限是高斯的并导致一个插件式置信区间。当可能存在多个最优策略时，我们使用不需要唯一性的子采样置信区间。该方法在两个补料分批案例研究中得到说明，其中在参数不确定性下优化进料速率曲线。
英文摘要：
Motivated by batch and semi-batch process operation, we study finite-horizon open-loop dynamic optimization problems with uncertain parameters. A common computational approach replaces the expected performance criterion by an average over finitely many sampled parameter realizations. We develop a statistical theory for the resulting sample-based optimal value as an estimator of the population optimal value. The analysis is based on a stability estimate showing that terminal losses depend Lipschitz continuously on the time-integrated control, which records the cumulative input delivered up to each time. This estimate yields a functional central limit theorem for the sample-based objective and a statistical limit theorem for the corresponding optimal value error. As a consequence, we obtain confidence intervals for the population optimal value. When the population optimizer is unique, the limit is Gaussian and leads to a plug-in confidence interval. When multiple optimal policies may exist, we use a subsampling confidence interval that does not require uniqueness. The methodology is illustrated on two fed-batch case studies in which feed-rate profiles are optimized under parametric uncertainty.
