Abstract:

We consider the optimal control problem of linear systems under information constraints and exhibit the effects of various information structures on the development of optimal control policies. We first consider a centralized setup. In this direction, a random-time state-dependent drift characterization for stability of Markov Chains will be introduced. This, when applied to a class of adaptive encoders used for controlling a linear system over a channel, leads to stochastic stability for the state. Once stability is obtained, we characterize optimal coding and control policies over a discrete channel with feedback under fully and partially observed cases. For the decentralized (multi-controller) case, we revisit the notion of (partial) nestedness of team decision theory. Communication requirements for nestedness require exchange of large data noiselessly, as such, are impractical. To address this, we introduce a weaker notion, stochastic nestedness, identifying sufficient statistics in the problem. This leads to optimal solutions under decentralized information constraints for a large class of problems. One example of this is the belief sharing information pattern. Some explicit examples will be provided. Part of this work is joint with Sean Meyn (University of Illinois).

Biography:

Serdar Yuksel received his BSc degree in Electrical and Electronics Engineering from Bilkent University, Ankara in 2001; MS and PhD degrees in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign in 2003 and 2006, respectively. He was a post-doctoral researcher at Yale University before joining Queen's University, Canada, as an assistant professor of Mathematics and Engineering in the Department of Mathematics and Statistics in 2007. His research interests are on control theory and information theory.