Side-information in control and estimation

As in portfolio theory, we can think of the value of side-information in a control system as the change in the “growth rate” due to side-information. A scalar counterexample (motivated by carry-free deterministic models) shows the value of side-information for control does not exactly parallel the value of side-information for portfolios. Mutual-information does not seem to be a bound here. The concept is further explored through a spinning vector control system that is re-oriented at each time so that the control or observation direction is partially unknown. The value of side-information can be calculated in this setup and it behaves quite differently in a control vs. estimation context. A second example considers the problem of vector control over a (scalar) erasure channel, the dual problem to the estimation problem of intermittent Kalman Filtering. The value of information here is measured through the change in the critical packet-drop probability for the system. While non-causal side-information regarding the packet arrivals does not affect the critical probability for the estimation problem, we find that it can generically be very valuable for the control problem - it seems to change the scaling behavior for the control counterpart to what would be considered the “high SNR limit” in communication problems.