CHARACTERIZATION OF WORST-CASE UNCERTAINTY GEOMETRY IN THE THEORY OF PROBABILISTIC ROBUSTNESS

摘要

In the newly emerging theory of probabilistic robustness, a class of admissible parameter distributions F is denned and the risk of performance violation is maximized; or equivalently, the probability of performance satisfaction is minimized. Within this new framework, the following fundamental question is the focal point of this paper: Given the total volume v > 0 of the "bad" parameter set X, what geometry of X and associated density f ∈ F lead to the highest possible risk? A rigorous description of this Worst- CaseUncertainty Geometry Problem is given in this paper and a solution is provided. Since the geometrical interpretation of the solution involves "wrapping" the uncertainty around an apriori robustness box, the name Wrapping Theorem is used to describe the main result.