September 26, 2012, ESB 2001

By nature or by design randomness is inherent to several dynamics of network coordination. In this talk, I will consider random linear dynamics, which may be designed to approximate average consensus, or may describe evolving opinions in social networks. Among these dynamics, there are several examples in which randomness induces a deviation between the average of the initial conditions and the actual convergence value. I will show that, under mild conditions on the distribution of the update matrices, the expected deviation has an upper bound which is inversely proportional to the size of the network. This result has been obtained in collaboration with J.M. Hendrickx.

Paolo Frasca received the Ph.D. degree in Applied Mathematics from Politecnico di Torino, Italy, in 2009. His research interests include mathematical control theory, focusing on networked and cyber-physical systems.