The Effect of Time Delay on the Average Data Rate and Performance in Networked Control Systems

TL;DR

This paper analyzes how transmission delay affects the minimum data rate needed for desired control performance in networked control systems, providing bounds and demonstrating the impact of delay on data rate requirements.

Contribution

It derives bounds on the minimum average data rate for control performance under delay and proposes coding schemes that approach these bounds for constant delays.

Findings

Higher delays increase the required data rate for a given performance.

The proposed coding schemes achieve near-optimal rates within 1.254 bits/sample of the lower bound.

Bounds and operational rates grow with increasing delay.

Abstract

This paper studies the performance of a feedback control loop closed via an error-free digital communication channel with transmission delay. The system comprises a discrete-time noisy linear time-invariant (LTI) plant whose single measurement output is mapped into its single control input by a causal, but otherwise arbitrary, coding and control scheme. We consider a single-input multiple-output (SIMO) channel between the encoder-controller and the decoder-controller which is lossless and imposes random time delay. We derive a lower bound on the minimum average feedback data rate that guarantees achieving a certain level of average quadratic performance over all possible realizations of the random delay. For the special case of a constant channel delay, we obtain an upper bound by proposing linear source-coding schemes that attain desired performance levels with rates that are at most 1.254 bits per sample greater than the lower bound. We give a numerical example demonstrating that bounds and operational rates are increasing functions of the constant delay. In other words, to achieve a specific performance level, greater channel delay necessitates spending higher data rate.