Trade-off between the sampling rate and the data accuracy

In this paper, we investigate the trade-off between the sampling rate and the data accuracy as a simplified model for resource allocation between different components of a networked control system. The problem is set up as the classical Linear Quadratic Gaussian (LQG) control problem of a sampled-data system over a discrete-time communication channel. We show that the LQG cost can be divided into the control cost, the communication cost, and the sampling cost. Through numerical examples, we demonstrate that the controller prefers to have more frequent communication with the plant, even if the information is crude instead of to obtain a piece of more precise information with a long delay. The main contribution of this paper is to provide a method to evaluate the time value of information in a control system.