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.