Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. In this talk, we present a “non-coherent” system where this strategy cannot work and provide an alternative strategy. We consider the estimation and control of a discrete-time linear system with continuous random observation gain, i.e. through a non-coherent channel. We will show such an unstable system is not mean-squared observable regardless of the density of the random observation gain: the mean-squared estimation error for any estimator must go to infinity. This is surprising in the context of threshold results for rate-limited estimation. In contrast to other results with rate-limited feedback, we show that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is not mean-square observable. Finally, carry-free models (generalized deterministic models) provide an intuitive interpretation for the results.
Gireeja Ranade is a PhD student in Electrical Engineering and Computer Science (EECS) at the University of California, Berkeley, working with Prof. Anant Sahai. She received her MS in EECS from UC Berkeley in 2009 and BS in EECS from the Massachusetts Institute of Technology in 2007. Her research interests broadly include information theory, decentralized control, and social and economic systems.