Stochastic Adventures in Systems and Controls

Abstract

Probability theory has had a significant impact on systems and controls. In this talk, we will visit three developments in control theory that has a close connection to, and impacted by, the results in probability theory. We discuss Perron-Frobenius Theorem and its relation to the results in distributed computation and optimization, and its generalization to time-varying chains. We will discuss a result in controllability of random networks and show how the recent developments in random matrix theory and inverse Littlewood-Offord Theory shed light on such problems. Lastly, we discuss controllability of safety-critical stochastic systems and how Martingale theory leads to design and analysis of control policies for stochastic systems.