Information Performance Tradeoffs in Control

TL;DR

This paper investigates the fundamental tradeoffs between control performance and communication constraints in networked control systems using information theory, covering AWGN channels, limited data rates, and systems with uncertainties.

Contribution

It provides a unified information-theoretic analysis of control performance under various communication constraints, including tight bounds and the effectiveness of simple quantization schemes.

Findings

Entropy of quantizer output affects control performance.

Channel SNR impacts system performance in AWGN channels.

Uniform quantization closely approaches theoretical rate-distortion bounds.

Abstract

We focus our attention on the most common scenario in networked control systems where the measured output from the observer is transmitted via a communication channel to the controller. Using information theoretic results, we studied the tradeoff between the performance and the accuracy of observations due to communication constraints for such a scenario. We focused on three important cases in the communication channel, the additive white Gaussian noise (AWGN), limited data rate and systems with multiplicative uncertainty in the system parameters. Using known theoretical results for a rate limited communication channel, we showed the effect of entropy of the output of quantizer on the control performance. The same was done for the case of multiplicative uncertainty in the system . For an AWGN channel, we showed the effect of channel SNR on the performance. For the analog joint source channel coding approach (which works only for Gaussian disturbances in the system), we showed that the known lower bound is tight even for non Gaussian system disturbances. We also compared the simulated performance of a system with known upper and lower rate distortion bounds for all the three cases. The lower bound on the rate is closely approached by a simple uniform quantization scheme, hence demonstrating its tightness.