Robustness metrics for dynamic optimization models under parameter uncertainty

Recent research in process systems engineering has focused mostly on the issue of making decisions under uncertainty. Various approaches used over the years include optimizing the expected and worst cases, maximizing the feasibility of operation, and constraining variances of performance measures. The consideration of robustness, that is, guaranteeing a reasonable performance over a wide range of uncertainty, is either implicit or explicit in these approaches, and is certainly receiving more attention. In this article, we argue that mathematical techniques for robust optimization must be capable of capturing different perspectives on risk of different users. We define some general robustness metrics that can represent significantly different robustness objectives simply by modifying functions and parameters. We also describe a solution procedure along with two illustrative examples.