Implicit communication in decentralized control systems
Abstract:
Decentralized control is a rich source of problems to explore the nature of information and information flows. I will narrow my perspective to how two approaches have recently paid dividends. The first is to take a "linear" approach to asking and answering questions. Aside from the advantage of compatibility with the traditional body of knowledge in control, this approach forces us to think about the units used for measuring information --- they change from the traditional "bits" to "dimensions." A somewhat unexpected connection emerges: LTI decentralized control is intimately connected to linear network coding! The second approach is to use linear deterministic models (pioneered by Avestimehr, Diggavi, and Tse) as a way to get an approximate handle on the "nonlinearity" required in decentralized systems by focusing on the implicit communication required. This approach helped us get some positive results on the (essentially single-shot) Witsenhausen Counterexample and recently, we have been able to extend this understanding to the more traditional infinite-horizon average-cost setting. (The bulk of this talk will be joint work with my student Se Yong Park, whose talk later in this program will go deeper into some of this.)