Parise, Francesca - Dal Col, Laura - Chiuso, Alessandro - Laurenti, Nicola - Schenato, Luca - Zanella, Andrea (2012) LQG control subject to intermittent observations and SNR limitations. [Rapporto tecnico] (Inedito)
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In this paper we consider the problem controlling unstable stochastic linear systems in the presence of a communication channel between the sensors and the actuators. We propose an LQG architecture that separates the problem of designing suitable regulators for controlling the plant, referred as Plant encoder/decoders, from the problem of designing encoder/decoder for channel transmissions. We provide a mathematical model that takes into account the most important features of today's current communication protocols such as quantization errors, limited channel capacity, decoding delay and packet loss, while still being amenable for analytic treatment. We then restrict to a special class of linear plant encoder/decoders and to a channel with signal-to-noise (SNR) limitations and packet loss only and we derive stability conditions and optimal design parameters for the controller. Through this analysis we are able to recover several results available in the literature that treated packet loss and quantization error separately.
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