Abstract
We provide an overview and some recent results on real-time communication and control over Gaussian channels. In particular, the problem of remote stabilization of linear systems driven by Gaussian noise over Gaussian relay channels is considered. Necessary and sufficient conditions for the mean-square stabilization are presented, which reveal signal-to-noise ratio requirements for stabilization which are tight in a certain class of settings. Optimal linear policies are constructed, global optimality and sub-optimality of such policies are investigated in a variety of settings. We also consider the design of low-delay sensing and transmit schemes for real-time communication.
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Acknowledgements
We would like to thank the editors, B. Bernhardsson, G. Como, and A. Rantzer, for giving us an opportunity to write this chapter. We are also very grateful to Johanness Kron (formerly Johanness Karlsson) for performing numerical simulations to generate the figures included in Sect. 2.6 of this chapter. Some of these results are part of his PhD thesis.
This research was supported by LCCC—Linnaeus Grant VR 2007-8646, Swedish Research Council.
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Zaidi, A.A., Oechtering, T.J., Yüksel, S., Skoglund, M. (2014). Stabilization and Control over Gaussian Networks. In: Como, G., Bernhardsson, B., Rantzer, A. (eds) Information and Control in Networks. Lecture Notes in Control and Information Sciences, vol 450. Springer, Cham. https://doi.org/10.1007/978-3-319-02150-8_2
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