TechFest Workshop - Theory Day - Session 2

Опубликовано 11 августа 2016, 7:43

Gireeja Ranade - A tiger by the tail: When multiplicative noise stymies control Consider an unstable discrete-time scalar linear system that is observed over a channel corrupted by continuous multiplicative noise. It was known that such a system can be stabilized using a simple linear strategy if the system growth is not too large (the threshold depends on the noise parameters). However, it was not clear whether non-linear controllers could overcome arbitrarily large growth factors. We use a non-standard approach to prove a converse: If the system growth is large enough, then system cannot be stabilized by any control strategy. One difficulty with multiplicative noise is that the mutual information per round between the system state and the observation is potentially unbounded. We handle this by providing the controller with side information about the magnitude of the state. (Joint work with Jian Ding and Yuval Peres.)