Analysis and control of large-scale stochastic networks is a problem of significant interest for engineering and natural science applications. Examples include electric power grid, biological networks, multi-agent systems, social networks, and building systems. In this talk, we discover fundamental limitation results that arise in the control and estimation of nonlinear systems over uncertain networks. The fundamental limitation for stabilization and estimation is expressed in terms of the positive Lyapunov exponents for the open loop system and the uncertainty statistics. The results are used to study the problem of synchronization in large-scale network systems with stochastic uncertainty in interactions. The main contribution is to provide analytical relationships for the interplay of roles played by the internal dynamics of the agents, network topology, and uncertainty statistics for network synchronization. The analytical characterization allows one to understand precise trade-off between the various network parameters necessary to achieve synchronization. In particular, for nearest neighbor networks with stochastic uncertainty in interactions, we show there exists an optimal number of neighbors with a maximum synchronization margin. This proves in the presence of interaction uncertainty, too many connections among network components are just as harmful for synchronization as the lack of connection.
Dr. Umesh Vaidya is Associate Professor in the Department of Electrical and Computer Engineering at Iowa State University, Ames IA, USA. He received the PhD degree in Mechanical Engineering Department from University of California Santa Barbara, CA, USA in 2004. He was Research Engineer at United Technologies Research Center (UTRC) East Hartford, CT, USA. He is recipient of 2012 National Science Foundation CAREER award. His research interest is in the area of network controlled dynamical systems with applications to power systems, building systems, and aerospace systems.