Time-invariant Prefix Coding for LQG Control

Abstract

Motivated by control with communication constraints, in this work we develop a time-invariant data compression architecture for linear-quadratic-Gaussian (LQG) control with minimum bitrate prefix-free feedback. For any fixed control performance, the approach we propose nearly achieves known directed information (DI) lower bounds on the time-average expected codeword length. We refine the analysis of a classical achievability approach, which required quantized plant measurements to be encoded via a time-varying lossless source code. We prove that the sequence of random variables describing the quantizations has a limiting distribution and that the quantizations may be encoded with a fixed source code optimized for this distribution without added time-asymptotic redundancy. Our result follows from analyzing the long-term stochastic behavior of the system, and permits us to additionally guarantee that the time-average codeword length (as opposed to expected length) is almost surely within a few bits of the minimum DI. To our knowledge, this time-invariant achievability result is the first in the literature. The originally published version of the supplementary material included a proof that contained an error that turned out to be inconsequential. This updated preprint corrects this error, which originally appeared under Lemma A.7.

arXiv commentVersion as accepted to the IEEE Journal on Selected Areas in Information Theory (Special Issue on Modern Compression), modulo an additional correction to the proof of Lemma A.7. Official version: https://ieeexplore.ieee.org/document/10002900. 14 page main paper, 4 pages appendix, 3 figures

References in corpus (9)

• General state space Markov chains and MCMC algorithms
• Wireless Control for Smart Manufacturing: Recent Approaches and Open Challenges
• A Characterization of the Minimal Average Data Rate that Guarantees a Given Closed-Loop Performance Level
• Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
• Nonanticipative Rate Distortion Function and Relations to Filtering Theory
• Rate of Prefix-free Codes in LQG Control Systems
• On Stochastic Stability of a Class of non-Markovian Processes and Applications in Quantization
• Directed Data-Processing Inequalities for Systems with Feedback
• Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels