Lecture by Roberto Tempo

On March 13, 2006 professor Roberto Tempo delivered a lecture «Randomization of Uncertain Systems: A New Paradigm for Robust Control» at the Faculty of Computational Mathematics and Cybernetics of the Moscow State (Lomonosov) University.

Abstract: Randomization is a powerful tool systematically utilized in various research areas, including computer science and numerical analysis. On the other hand, randomization appears only in a rather scattered fashion within systems and control. For example, simulation techniques are largely based on Monte Carlo methods, but these techniques are often used with the sole objective of testing a specific system's performance, and not for deriving results applicable to broad classes of systems. Recently, for systems with uncertainty, we have seen a first attempt to rigorously develop efficient randomized algorithms with the goal of reducing the complexity of feedback. In this context, worst-case uncertainty bounds provided by robust control are merged with probabilistic information. That is, a certain probability measure is associated to the structured uncertainty entering into the system. This is indeed useful for analyzing the interplay between worst-case and probabilistic methods.

In this lecture, we address these issues and study some specific problems, such as the computation of bounds on the number of required random systems to guarantee a given probabilistic level, and the sequential solution of Lyapunov analysis and synthesis problems.