TY - JOUR
T1 - Control over Gaussian channels with and without source–channel separation
AU - Khina, Anatoly
AU - Gårding, Elias Riedel
AU - Pettersson, Gustav M.
AU - Kostina, Victoria
AU - Hassibi, Babak
N1 - KAUST Repository Item: Exported on 2022-06-13
Acknowledgements: This work was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant 708932. The work of E. Riedel Gårding was supported by the National Science Foundation (NSF) under Grant CCF-1566567 through the SURF program. The work of G. M. Pettersson was supported by The Boeing Company under the SURF program. The work of V. Kostina was supported in part by the NSF under Grant CCF-1566567. The work of B. Hassibi was supported in part by the NSF under Grant CNS-0932428, Grant CCF-1018927, Grant CCF-1423663, and Grant CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and by King Abdullah University of Science and Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2019/4/19
Y1 - 2019/4/19
N2 - We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source–channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon–Kotel’nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.
AB - We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source–channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon–Kotel’nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.
UR - http://hdl.handle.net/10754/678919
UR - https://ieeexplore.ieee.org/document/8693975/
UR - http://www.scopus.com/inward/record.url?scp=85074522089&partnerID=8YFLogxK
U2 - 10.1109/TAC.2019.2912255
DO - 10.1109/TAC.2019.2912255
M3 - Article
SN - 1558-2523
VL - 64
SP - 3690
EP - 3705
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 9
ER -