Many of today's robot applications depend on wireless communications, whose performance can impact the whole system. To support analysis of feedback control through limited channels, we develop describing functions (DFs) for three variations on the series interconnection of a quantizer, a binary erasure channel, and decoder for a single input single output (SISO) system. The key steps in our derivation hold when the decoder is a linear-quadratic-Gaussian (LQG)-type control, a zero-output decoder, or a hold-output decoder. We confirm the accuracy of the new formulas and provide an example showing limit cycle behavior.
Describing Functions for Scalar Information Channels Subject to Quantization and Packet Loss
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 4, 2013; final manuscript received January 30, 2015; published online March 23, 2015. Assoc. Editor: Evangelos Papadopoulos.
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Gilbertson, E., and Hover, F. (July 1, 2015). "Describing Functions for Scalar Information Channels Subject to Quantization and Packet Loss." ASME. J. Dyn. Sys., Meas., Control. July 2015; 137(7): 071006. https://doi.org/10.1115/1.4029717
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