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

• 成果类型: Article
• 署名作者: Barforooshan, Mohsen; Derpich, Milan S.; Stavrou, Photios A.; Ostergaard, Jan
• 署名单位: Aalborg University; Universidad Tecnica Federico Santa Maria; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047578
• 发表日期: 2022
• 页码: 16-31
• 关键词: Delays; Upper bound; entropy; Delay effects; Linear systems; Probability density function; Information rates; Data rate constraints; Information theory; networked control systems (NCSs); optimal control; time delay

摘要

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.