A Framework for Control System Design Subject to Average Data-Rate Constraints

Abstract

This paper studies discrete-time control systems subject to average data-rate limits. We focus on a situation where a noisy linear system has been designed assuming transparent feedback and, due to implementation constraints, a source-coding scheme (with unity signal transfer function) has to be deployed in the feedback path. For this situation, and by focusing on a class of source-coding schemes built around entropy coded dithered quantizers, we develop a framework to deal with average data-rate constraints in a tractable manner that combines ideas from both information and control theories. As an illustration of the uses of our framework, we apply it to study the interplay between stability and average data-rates in the considered architecture. It is shown that the proposed class of coding schemes can achieve mean square stability at average data-rates that are, at most, 1.254 bits per sample away from the absolute minimum rate for stability established by Nair and Evans. This rate penalty is compensated by the simplicity of our approach.

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

“…Zero-delay source coding is desirable in many applications, e.g., in real-time applications where one cannot afford to have large delays [1], or in systems involving feedback, in which the current input depends on the previous outputs [2]- [4]. A weaker notion closely related to the principle behind zero-delay codes is that of causal source coding, wherein the reproduction of the present source sample depends only on the present and past source samples but not on the future source samples [5], [6].…”

Real-Time Perceptual Moving-Horizon Multiple-Description Audio Coding

“…From (21), it may be observed that f w k ( ξ k ) has isocontours (level sets) that are shifted spheres in R N and centered at w k . Thus, for any ξ…”

“…Proof: Since we have a source coding system within a feedback loop, there is memory in the system and it follows from [20] (see also Theorem 1 in [21]), that the average entropy is lower bounded by Massey's notion of directed mutual information [22]. Thus,…”

Independent source coding for control over noiseless channels

“…Theorem 1: Consider a causal source coding scheme inside a feedback loop, as in Figure 1. Under suitable assumptions (see [3]), R ≥ I ∞ (y → u), where I ∞ (y → u) denotes the directed mutual information rate defined by Massey [5].…”

“…We study the minimal average data-rate that allows one to attain a given performance level (as measured by the stationary variance σ 2 e of e) in the considered NCS. (Details can be found in [3], [4] …”