Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

• Published in: IEEE transactions on automatic control Vol. 67; no. 8; pp. 3822 - 3835
• Main Authors: Stavrou, Photios A., Skoglund, Mikael, Tanaka, Takashi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Coding; Control systems; Discrete time systems; Distortion; Feedback control; Finite-time horizon; Gaussian process; Heuristic algorithms; Linear quadratic Gaussian control; Lower bounds; Markov processes; Optimal control; quantization; Rate-distortion; Resource description framework; reverse-waterfilling; sequential causal coding; Source coding; Stochastic processes; Stochastic systems; Upper bound; Upper bounds
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2021.3110430

In this article, we revisit the sequential source-coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion, for a given distortion level, at each instant of time and any fixed finite-time horizon. The idea behind this characterization facilitates the derivation of analytical , nonasymptotic , and finite-dimensional lower and upper bounds in two control-related scenarios: a) A parallel time-varying Gauss-Markov process with identically distributed spatial components that are quantized and transmitted through a noiseless channel to a minimum mean-squared error decoder; and b) a time-varying quantized linear quadratic Gaussian (LQG) closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our nonasymptotic lower bound on the quantized LQG control problem reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite-time horizon. We supplement our framework with illustrative simulation experiments.