RACT - Randomized Algorithms Control Toolbox: A Tutorial Introduction

Abstract

Probabilistic and randomized techniques for analysis of uncertain systems and design for robustly performing control systems have attracted considerable interest in recent years, and a significant amount of theoretical and algorithmic results have appeared in the literature. The starting idea in the probabilistic approach to the analysis of uncertain systems is to characterize the uncertain parameters as random variables, and then to evaluate the system performance in terms of probabilities. In an analogous sense, probabilistic synthesis is aimed at determining the design parameters so that certain desired levels of performance are attained with high probability. This probabilistic approach is complementary to the mainstream methods in robust control, which seek worst-case performance guarantees and consider the uncertainties as deterministic unknown-but-bounded quantities.