Randomized Algorithms for Analysis and Control of Uncertain Systems - With Applications

The main objective of this book is to introduce the reader to the fundamentals of the area of probabilistic and randomized methods for analysis and design of uncertain systems. The take off point of this research is the observation that many quantities of interest in engineering, which are generally very difficult to compute exactly, can be easily approximated by means of randomization. The contribution of this book is in the direction of proposing a new paradigm for control analysis and design, based on a rapprochement between the classical stochastic approach and the modern worst-case approach. Indeed, in our setting we shall assume that the uncertainty is confined in a set (as in the worst-case approach) but, in addition to this information, we consider it as a random variable with given multivariate probability distribution. A typical example is a vector of uncertain parameters uniformly distributed inside a ball of fixed radius. We address the interplay between stochastic (soft) and worst-case (hard) performance bounds for control system design in a rigorous fashion, with the goal to derive useful computational tools. The algorithms derived in this context are based on uncertainty randomization and are usually called randomized algorithms.