The Effect of Time Delay on the Average Data Rate and Performance in Networked Control Systems
For researchers in networked control systems, this work provides theoretical bounds linking delay and data rate, but the results are incremental as they extend known rate-distortion ideas to a specific delay model.
This paper studies the effect of random and constant time delays on the minimum average data rate required to achieve a given quadratic control performance in a networked control system. For constant delay, they derive an upper bound showing rates at most 1.254 bits/sample above the lower bound, and demonstrate numerically that higher delays require higher data rates.
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.