CIF: Small: Limitations of communication and control and over noisy feedback links

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The widespread availability of communication networks fosters interactions among nodes that constantly affect each other by exchanging information over the available communication links. This dynamic, interactive, aspect of communication is common to many networked systems, from social networks to biological networks. Its causal nature differs from the batch coding and processing of classical communication systems and is not handled well by the traditional information theory results. These settings are more appropriate for the functioning and the understanding of control and regulation processes and, more generally, processes of learning and adaptation.The main objective of the proposed research is to characterize the fundamental limitations of interacting dynamical systems over noisy communication links. We start analyzing the problem of interactive point-to-point communication where the encoder has access to noisy feedback from the receiver based on a new information theoretic quantity that captures the actual information flow in the forward channel when the feedback channel is noisy. From it, we propose to derive computable bounds on the noisy feedback capacity for common channels, to develop control-inspired practical coding schemes that are robust to noise in the feedback link, and to characterize costs and benefits of using noisy feedback. Further, we propose extensions of the theory to other new noisy feedback structures motivated by remote guidance and virtual reality applications. The resulting dynamical systems are both communication and control systems at the same time. We aim to study properties and limitations of these interacting dynamical systems, in an integrated way, by extending the relevant results in networked control systems.