On The Rate-Cost of Gaussian Linear Control Systems with Random Communication Delays
Jia Zhang, Chih-Chun Wang · 2018
This work considers Gaussian linear control systems where the goal is to guarantee system-state mean-square stability (i.e., E(||x(t)||2) ≤ D) while minimizing the traffic rate R between the sensor(s) and the controller. Most existing results either assume zero delay or focus on the asymptotic setting that overlooks the impact of delay. Nonetheless, in practice the communication delay is randomly distributed due to varying channel/network conditions. When the sensor measurement finally arrives at the controller, the age-of-information is thus random. Heuristically, an “old” measurement provides less valuable information than a “young” measurement but the quantitative impact of random delay on the optimal rate-cost tradeoff R*(D) remains an open problem. This work provides the first lower bound RLB(D) for the random delay setting and designs a simple scheme that leads to a numerically evaluated upper bound RUB(D). Jointly RLB(D) and RUB(D) bracket the optimal tradeoff R*(D). The new RLB(D) is asymptotically tight when either D→∞ or R→∞, and sheds further insights on how the (random) age of information could impact the performance of a cyber-physical control system.