Rice Grain Effect and Impacts of Message Size and Error on Networked Control Systems

In recent years, there has been a growing interest in investigating the interactions of communication and control in networked control systems (NCSs) or multiagent systems (MASs). Although extensive research has been explored on these interactions, most studies are oversimplified and idealized. Therefore, more in-depth and practical studies on communication in control systems are needed. Our study aims to explore the practical impacts of communication networks on control systems. We provide a general overhead analysis for the structure of NCSs and design an express delivery-based cost chart, referred to as an E-Chart, for the control message sizes. We found an effect in the express delivery service known as the “Rice Grain Effect,” defined as the cost of delivering a single rice grain is the same as the cost of delivering two rice grains. We apply the effect to the control overhead analysis and the E-Chart. We present the results of the E-Chart and the overhead under different message sizes and compression ratios; furthermore, we define a new metric to reflect the stability of the formation control and conduct simulations to study the impacts of message size and error on NCSs. In particular, formation control is affected by both bit error rate and message size, and the system exhibits high sensitivity to variations in bit error rate.