This paper presents a notion of \u201ccontrol capacity\u201d that gives a fundamental limit on the control of a system through an unreliable actuation channel. It tells us how fast we can reliably actively dissipate uncertainty in a system through that actuation channel. We give a computable single-letter characterization for scalar systems with memoryless stationary multiplicative actuation channels. The sense of control capacity is tight for answering questions of stabilizability for scalar linear systems \u2014 a system is stabilizable through an actuation channel if and only if the control capacity of that actuation channel is larger than the log of the unstable open-loop eigenvalue. For second-moment senses of stability, our result recovers the classic uncertainty-threshold principle result. However, our formulation can also deal with any other moment. The limits of higher and higher moment senses of stability correspond to a \u201czero-error\u201d sense of control capacity and taking the limit to weaker-and-weaker moments corresponds to a \u201cShannon\u201d sense of control capacity.<\/p>\n","protected":false},"excerpt":{"rendered":"
This paper presents a notion of \u201ccontrol capacity\u201d that gives a fundamental limit on the control of a system through an unreliable actuation channel. It tells us how fast we can reliably actively dissipate uncertainty in a system through that actuation channel. 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