Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels
For control engineers, this work provides theoretical lower bounds on data rates for networked control systems with delay, but the results are incremental as they extend known information-theoretic bounds to include constant delay.
The paper investigates the minimal average data rate required for output feedback control of a noisy LTI plant over a noiseless digital channel with transmission delay, showing that delay increases the needed data rate for a given performance level. Simulations demonstrate that operational data rates using a scalar uniform quantizer are within about 0.3 bits of the theoretical lower bounds.
The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.