A Characterization of the Minimal Average Data Rate that Guarantees a Given Closed-Loop Performance Level

TL;DR

This paper establishes a fundamental lower bound on the average data rate needed for networked control systems to meet specific performance criteria, and proposes a coding scheme close to this bound for noisy LTI plants.

Contribution

It introduces a lower bound on minimal average data rate for guaranteed control performance and presents a near-optimal coding scheme for noisy LTI systems.

Findings

Lower bound on data rate for desired performance

Coding scheme within 1.254 bits of the lower bound

Numerical example demonstrating the theoretical results

Abstract

This paper studies networked control systems closed over noiseless digital channels. By focusing on noisy LTI plants with scalar-valued control inputs and sensor outputs, we derive an absolute lower bound on the minimal average data rate that allows one to achieve a prescribed level of stationary performance under Gaussianity assumptions. We also present a simple coding scheme that allows one to achieve average data rates that are at most 1.254 bits away from the derived lower bound, while satisfying the performance constraint. Our results are given in terms of the solution to a stationary signal-to-noise ratio minimization problem and builds upon a recently proposed framework to deal with average data rate constraints in feedback systems. A numerical example is presented to illustrate our findings.