Communication for control
Anant Sahai, Se Yong Park and Pulkit Grover
National Science Foundation CCF-729122
Traditional information theory deals with communicating noninteractive messages, yet many real-world applications are inherently interactive in nature. Control theory provides us with models of interaction and it is natural to treat certain distributed control problems as having a communication problem embedded in them. Extending information theory to cover such cases gives us new insights into reliable communication, feedback, and interaction.
Recently, we have used this to get new insights into the long-standing Witsenhausen counterexample in distributed control -- by showing how it is intimately related to a family of seemingly unrelated information-theoretic problems.
We solve the Witsenhausen counterexample (and its vector extensions) to within a constant factor uniformly over all problem parameters, providing the first provably approximately optimal result for the problem.
We also show that our techniques are applicable to more general problems by considering extensions of Witsenhausen's counterexample with a) costs on all states and inputs, and b) noises in the observation of both controllers.