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Optimal Downlink-Uplink Scheduling of Wireless Networked Control for Industrial IoT

Kang Huang, Wanchun Liu, Yonghui Li, Branka Vucetic, Andrey Savkin

TL;DR

This article considers a practical half-duplex (HD) controller, which introduces a novel transmission-scheduling problem for WNCSs, and derives an easy-to-compute suboptimal policy, which notably reduces the average cost of the plant compared to a naive alternative- scheduling policy.

Abstract

This paper considers a wireless networked control system (WNCS) consisting of a dynamic system to be controlled (i.e., a plant), a sensor, an actuator and a remote controller for mission-critical Industrial Internet of Things (IIoT) applications. A WNCS has two types of wireless transmissions, i.e., the sensor's measurement transmission to the controller and the controller's command transmission to the actuator. In this work, we consider a practical half-duplex controller, which introduces a novel transmission-scheduling problem for WNCSs. A frequent scheduling of sensor's transmission results in a better estimation of plant states at the controller and thus a higher quality of control command, but it leads to a less frequent/timely control of the plant. Therefore, considering the overall control performance of the plant in terms of its average cost function, there exists a fundamental tradeoff between the sensor's and the controller's transmissions. We formulate a new problem to optimize the transmission-scheduling policy for minimizing the long-term average cost function. We derive the necessary and sufficient condition of the existence of a stationary and deterministic optimal policy that results in a bounded average cost in terms of the transmission reliabilities of the sensor-to-controller and controller-to-actuator channels. Also, we derive an easy-to-compute suboptimal policy, which notably reduces the average cost of the plant compared to a naive alternative-scheduling policy.

Optimal Downlink-Uplink Scheduling of Wireless Networked Control for Industrial IoT

TL;DR

This article considers a practical half-duplex (HD) controller, which introduces a novel transmission-scheduling problem for WNCSs, and derives an easy-to-compute suboptimal policy, which notably reduces the average cost of the plant compared to a naive alternative- scheduling policy.

Abstract

This paper considers a wireless networked control system (WNCS) consisting of a dynamic system to be controlled (i.e., a plant), a sensor, an actuator and a remote controller for mission-critical Industrial Internet of Things (IIoT) applications. A WNCS has two types of wireless transmissions, i.e., the sensor's measurement transmission to the controller and the controller's command transmission to the actuator. In this work, we consider a practical half-duplex controller, which introduces a novel transmission-scheduling problem for WNCSs. A frequent scheduling of sensor's transmission results in a better estimation of plant states at the controller and thus a higher quality of control command, but it leads to a less frequent/timely control of the plant. Therefore, considering the overall control performance of the plant in terms of its average cost function, there exists a fundamental tradeoff between the sensor's and the controller's transmissions. We formulate a new problem to optimize the transmission-scheduling policy for minimizing the long-term average cost function. We derive the necessary and sufficient condition of the existence of a stationary and deterministic optimal policy that results in a bounded average cost in terms of the transmission reliabilities of the sensor-to-controller and controller-to-actuator channels. Also, we derive an easy-to-compute suboptimal policy, which notably reduces the average cost of the plant compared to a naive alternative-scheduling policy.

Paper Structure

This paper contains 32 sections, 9 theorems, 80 equations, 12 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamic Plant
  4. HD Operation of the Controller
  5. Wireless Channel
  6. Optimal Plant-State Estimation
  7. $v$-Step Predictive Plant-State Control
  8. Analysis of the Downlink-Uplink Scheduling
  9. Estimation-Error Covariance
  10. Plant-State Covariance of One-Step Controllable Case
  11. Plant-State Covariance of $v$-Step Controllable Case
  12. Problem Formulation
  13. One-Step Controllable Case: Optimal Transmission-Scheduling Policy
  14. MDP Formulation
  15. Existence of the Optimal Scheduling Policy
  16. ...and 17 more sections

Key Result

Proposition 1

The plant-state covariance $\mathbf{P}_{k}$ in time slot $k$ is where the summation operator has the property that $\sum_{i=a}^{b} (\cdot)=0$ if $a>b$, $\mathbf{F}(\cdot)$ is defined in F, and

Figures (12)

  • Figure 1: The system architecture.
  • Figure 2: Illustration of the state parameters, where red vertical bars denote successful controller's transmissions and blue vertical bars denote the most recent successful sensor's transmissions prior to the successful controller's transmissions.
  • Figure 3: The state space $\mathbb{S}$ (shaded dots) of the MDP.
  • Figure 4: Temperature and humidity control in grain conservation.
  • Figure 5: The uplink-downlink scheduling policies, where where 'o' and '.' denote $a = 1$ and $a = 2$, respectively, and 'x' denotes a state that does not belong to $\mathbb{S}$.
  • ...and 7 more figures

Theorems & Definitions (25)

  • Definition 1: Closed-loop Stability demirel2017tradeschenato2007foundations
  • Example 1
  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • ...and 15 more