Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

• 成果类型: Article
• 署名作者: Stavrou, Photios A.; Skoglund, Mikael; Tanaka, Takashi
• 署名单位: Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3110430
• 发表日期: 2022
• 页码: 3822-3835
• 关键词: Distortion; Upper bound; source coding; Markov processes; Heuristic algorithms; Resource description framework; Rate-distortion; Finite-time horizon; QUANTIZATION; reverse-waterfilling; sequential causal coding; Stochastic systems

摘要

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.