Date: Sep. 10 at 3:30 in 3355 Engineering Hall Title: Probabilistic Robustness: A New Line of Research Speaker: Bob Barmish, ECE Department Abstract: Many open robustness analysis problems are known to have high computational complexity. Often, such problems formally qualify as being ``NP-Hard'' and this is generally understood to mean that it will be difficult to make major progress. The new line of research, to be described in this seminar, addresses this issue. Via a slight change in the problem formulation, it often becomes possible to obtain simple solution techniques while preserving the essence of the underlying engineering objectives. This is accomplished by embedding the classical robustness problem into a more general probabilistic framework. In this new setting, if one is willing to accept a small well-defined risk of performance violation, many robustness problems not only become easier to solve but it is also possible achieve a significant increase in the tolerable radius of uncertainty --- over and above the radius provided by classical robustness theory. The most salient feature of the new line of research is the absence of any serious apriori assumption about the statistics of the uncertain parameters. As in classical robustness theory, only interval bounds are assumed for each parameter and the (unknown) underlying density function is only required to satisfy a certain physically motivated monotonicity condition. In addition to describing this new paradigm for dealing with uncertainty, this seminar also includes an overview of the results obtained to date and new directions for further work are suggested.