On the Latency, Rate and Reliability Tradeoff in Wireless Networked Control Systems for IIoT

TL;DR

This article focuses on a WNCS, where a controller transmits quantized and encoded control codewords to a remote actuator through a wireless channel, and adopts a detailed model of the wireless communication system, which jointly considers the interrelated communication parameters.

Abstract

Wireless networked control systems (WNCSs) provide a key enabling technique for Industry Internet of Things (IIoT). However, in the literature of WNCSs, most of the research focuses on the control perspective, and has considered oversimplified models of wireless communications which do not capture the key parameters of a practical wireless communication system, such as latency, data rate and reliability. In this paper, we focus on a WNCS, where a controller transmits quantized and encoded control codewords to a remote actuator through a wireless channel, and adopt a detailed model of the wireless communication system, which jointly considers the inter-related communication parameters. We derive the stability region of the WNCS. If and only if the tuple of the communication parameters lies in the region, the average cost function, i.e., a performance metric of the WNCS, is bounded. We further obtain a necessary and sufficient condition under which the stability region is $n$-bounded, where $n$ is the control codeword blocklength. We also analyze the average cost function of the WNCS. Such analysis is non-trivial because the finite-bit control-signal quantizer introduces a non-linear and discontinuous quantization function which makes the performance analysis very difficult. We derive tight upper and lower bounds on the average cost function in terms of latency, data rate and reliability. Our analytical results provide important insights into the design of the optimal parameters to minimize the average cost within the stability region.

Figures (8)

• Figure 1: An illustration of the WNCS, where $x_t$, $\tilde{\mu}_t$, $u_t$, $s_t$ and $w_t$ are the plant state, the control signal, the control action, the feedback signal and the disturbance at time $t$, respectively. $a$ and $b$ are the parameters of the plant system.
• Figure 2: The stability region of a plant in terms of the data rate and the blocklength, where $a = 2.1$ and $b=1$. The bounded dark colored region and the unbounded moderate and light colored regions are plotted at $\mathsf{SNR} = 10$, $11$ and $20$ dB, respectively.
• Figure 3: Illustration of the plant state, $x_t$, and the correctness of the codeword decoding, when $n=3$.
• Figure 4: Illustration of the patterns.
• Figure 5: Comparison of stability regions achieved by different control and quantization policies with $\mathsf{SNR}=30$ dB and $a=2.1$.

Theorems & Definitions (14)

• Remark 1
• Lemma 1
• proof
• Definition 1: Stability Region
• Corollary 1
• Remark 2
• Proposition 1
• proof
• Remark 3
• Proposition 2