In this talk, we visit three systems and controls problems with stochastic components. The first problem, relates to the control of a safety critical autonomous vehicle. We provide a necessary and sufficient condition reachability result for an open and bounded safety set. In particular, we show that a stochastic system is controllable if and only if the expected system is controllable.
The second problem relates to control of large networked systems. We prove that a conjecture of Chris Godsil on controllability of graphs is true. The conjecture asserts that the number of binary symmetric matrices A that are controllable with all-one vector to the total number of binary matrices approaches one as the dimension of A approaches infinity. We also provide a result on universality of minimal controllability of networked systems.
Finally, time permitting, we will discuss a generalization of Perron–Frobenius theorem to products of time-varying random stochastic matrices and we discuss some of its applications in distributed control, optimization, and the study of opinion dynamics.
Behrouz Touri is an Assistant Professor of the Electrical, Computer, and Energy Engineering Department at the University of Colorado Boulder. He received his B.Sc. degree in Electrical Engineering from Isfahan University of Technology, Isfahan, Iran in 2006, his M.Sc. degree in Communications, Systems, Electronics from Jacobs University, Bremen, Germany in 2008, and his Ph.D. degree in Industrial Engineering from the University of Illinois at Urbana-Champaign in 2011. Between 2011 and 2014, he was a postdoctoral researcher with the ECE department of the University of Illinois and Georgia Institute of Technology. His research interests include applied probability theory, distributed optimization, control and estimation, population dynamics, and evolutionary game theory. He is a recipient of AFOSR 2016 Young Investigator Award for his work on structural approach to distributed optimization.