As in portfolio theory, we can think of the value of side-information in a control system as the change in the \u201cgrowth rate\u201d 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 sideinformation 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 \u2014 it seems to change the scaling behavior for the control counterpart to what would be considered the \u201chigh SNR limit\u201d in communication problems<\/p>\n","protected":false},"excerpt":{"rendered":"
As in portfolio theory, we can think of the value of side-information in a control system as the change in the \u201cgrowth rate\u201d 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 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