The Effect of Time Delay on the Average Data Rate and Performance in Networked Control Systems

• Published in: IEEE transactions on automatic control Vol. 67; no. 1; pp. 16 - 31
• Main Authors: Barforooshan, Mohsen, Derpich, Milan S., Stavrou, Photios A., Ostergaard, Jan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel coding; Coders; Coding; Controllers; Data rate constraints; Delay control systems; Delay effects; Delays; Digital communication channels; Digital communication systems; Discrete time control systems; Discrete time systems; Entropy; Feedback; Feedback control; Feedback control loops; Increasing functions; Information rates; information theory; Linear control systems; Linear systems; Linear time invariant; Lower bounds; Network control; Networked control systems; networked control systems (NCSs); Numerical experiments; optimal control; Probability density function; Random time delay; Single input multiple output channel; time delay; Time lag; Timing circuits; Transmission delays; Upper bound; Upper bounds
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2020.3047578

This article 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 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 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 b per sample greater than the lower bound. We supplement our results with a numerical experiment demonstrating that the obtained bounds and operational rates are increasing functions of the constant delay.