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Wireless Networked Control Systems with Coding-Free Data Transmission for Industrial IoT

Wanchun Liu, Petar Popovski, Yonghui Li, Branka Vucetic

TL;DR

This article forms a power allocation problem to optimize the sum cost functions of multiple plants, subject to the plant stabilization condition and the controller’s power limit, and derives a closed-form solution, which indicates that the optimal power allocation policy for stabilizing the plants with different channel conditions is reminiscent of the channel-inversion policy.

Abstract

Wireless networked control systems for the Industrial Internet of Things (IIoT) require low latency communication techniques that are very reliable and resilient. In this paper, we investigate a coding-free control method to achieve ultra-low latency communications in single-controller-multi-plant networked control systems for both slow and fast fading channels. We formulate a power allocation problem to optimize the sum cost functions of multiple plants, subject to the plant stabilization condition and the controller's power limit. Although the optimization problem is a non-convex one, we derive a closed-form solution, which indicates that the optimal power allocation policy for stabilizing the plants with different channel conditions is reminiscent of the channel-inversion policy. We numerically compare the performance of the proposed coding-free control method and the conventional coding-based control methods in terms of the control performance (i.e., the cost function) of a plant, which shows that the coding-free method is superior in a practical range of SNRs.

Wireless Networked Control Systems with Coding-Free Data Transmission for Industrial IoT

TL;DR

This article forms a power allocation problem to optimize the sum cost functions of multiple plants, subject to the plant stabilization condition and the controller’s power limit, and derives a closed-form solution, which indicates that the optimal power allocation policy for stabilizing the plants with different channel conditions is reminiscent of the channel-inversion policy.

Abstract

Wireless networked control systems for the Industrial Internet of Things (IIoT) require low latency communication techniques that are very reliable and resilient. In this paper, we investigate a coding-free control method to achieve ultra-low latency communications in single-controller-multi-plant networked control systems for both slow and fast fading channels. We formulate a power allocation problem to optimize the sum cost functions of multiple plants, subject to the plant stabilization condition and the controller's power limit. Although the optimization problem is a non-convex one, we derive a closed-form solution, which indicates that the optimal power allocation policy for stabilizing the plants with different channel conditions is reminiscent of the channel-inversion policy. We numerically compare the performance of the proposed coding-free control method and the conventional coding-based control methods in terms of the control performance (i.e., the cost function) of a plant, which shows that the coding-free method is superior in a practical range of SNRs.

Paper Structure

This paper contains 25 sections, 7 theorems, 61 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions
  5. System Model
  6. Coding-Free Control Protocol
  7. Wireless Communication Channels
  8. Control Action
  9. Plant Under Control and Performance Metrics
  10. Slow-Fading-Single-Plant Case: Analysis and Optimization
  11. Slow-Fading-Multi-Plant Case: Optimal Design
  12. Joint Controller-Actuator Optimization
  13. Optimal Design with Identical Actuator Factors
  14. Optimal Design with Identical Controller Factors
  15. Fast-Fading Case: Analysis and Optimization
  16. ...and 10 more sections

Key Result

Theorem 1

In the slow-fading-single-plant scenario, the optimal cost of the plant and the optimal controller and actuator factors for coding-free control are given as

Figures (10)

  • Figure 1: A wireless networked control system (WNCS).
  • Figure 2: Illustration of an $M_0$-plant WNCS.
  • Figure 3: Coding-free control protocol for plant $i$.
  • Figure 4: Illustration of $\mathsf{E}_{\!}\left[ x^2_i(t) \right]$ and $\mathsf{SNR}_i$ versus $\tilde{K}_i$.
  • Figure 5: The plant state $x(t)$ and the average cost function in term of the number of control symbols with different closed-loop parameter $A_c$.
  • ...and 5 more figures

Theorems & Definitions (15)

  • Definition 1: Stability condition in slow-fading channel
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Remark 3
  • Proposition 1
  • Remark 4
  • Proposition 2
  • Remark 5
  • ...and 5 more