This talk will address the problem of quantifying the expected value of some function of a random variable with unknown distribution. Typical problems of this type include determining the expected profit of a stock portfolio with uncertain returns and quantifying the symbol error rate in a noisy communication channel. In particular, the talk will address cases in which only limited or ambiguous moment information is available, but some additional structural properties – e.g. symmetry, unimodality or monotonicity – are known to hold. In such cases, one can compute a sharp upper bound on the worst-case expectation, taken over all distributions satisfying the partial moment and other structural information available.  The results can also be applied to control of linear systems with chance constraints, for which robust conditional Value-at-Risk (CVaR) conditions can be used to control both the probability and the degree of constraint violations.

Paul Goulart is an Associate Professor in Control Engineering in the University of Oxford. From 2011 to 2014 he was a senior researcher in the Automatic Control Laboratory at ETH Zurich, and from 2007 to 2011 a lecturer in control systems in the Department of Aeronautics at Imperial College London.  He received BSc and MSc degrees in Aeronautics and Astronautics from the Massachusetts Institute of Technology (MIT). He was selected as a Gates Scholar at the University of Cambridge, where he received a PhD in Control Engineering in 2007. His research interests include model predictive control, robust optimization and control of fluid flows.