Control With Side Information

This paper develops an information-theoretic understanding of side information in control systems. We build on the notion of “control capacity” — the rate at which a controller can dissipate uncertainty in a system over an actuation channel — and quantify the change in control capacity due to side information. The results build on the bit-level carry-free models that are widely used to understand information flows in wireless network information theory. These models motivate our definitions and theorems. We show that we are able to compute the value of side information for real i.i.d. actuation channels using a simple conditional expectation. Finally, we give an example of how side information affects the control capacity of an actuation channel with a uniform distribution.