The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems
By Anant Sahai, Sanjoy K. Mitter. IEEE Transactions on Information Theory, 2006
438 citations recorded by the source corpus.
In this paper, we review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called "anytime capacity" is necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk-Kailath scheme for communication over the additive white Gaussian noise (AWGN) channel with feedback. In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy
Subfields: Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/ef43272b6d1a30d9b9ecd1227744dc88051512e7
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In Computer Networks and Communications
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In Control and Systems Engineering
Citations in the corpus
- Feedback stabilization over signal-to-noise ratio constrained channels (2004, background): “As discussed in [22], Shannon capacity is a “tight” channel figure of merit to characterize the equivalence between feedback stability and reliable communication in the case of AWGN channels.”
- Cyber–Physical Systems: A Perspective at the Centennial (2012, background): “The concept of anytime capacity is introduced in [73] to capture a noisy communication channel when it is used as part of a”