Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties

One purpose of the "Historical Perspectives" column is to look back at work done by pioneers in control and related fields that has been neglected for many years but was later revived in the control literature. This column discusses the topic of Norbert Wiener's most cited paper, which proposed polynomial chaos expansions (PCEs) as a method for probabilistic uncertainty quantification in nonlinear dynamical systems. PCEs were almost completely ignored until the turn of the new millennium, when they rather suddenly attracted a huge amount of interest in the noncontrol literature. Although the control engineering community has studied uncertain systems for decades, all but a handful of researchers in the systems and control community have ignored PCEs. The purpose of this column is to present a concise introduction to PCEs, provide an overview of the theory and applications of PCE methods in the control literature, and to consider the question of why PCEs have only recently appeared in the control literature.