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Wireless Feedback Control with Variable Packet Length for Industrial IoT

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

TL;DR

This letter proposes a novel WNCS, where the controller adaptively changes the packet length for control based on the current status of the physical process, and formulate a decision-making problem and finds the optimal variable-length packet-transmission policy for minimizing the long-term average cost of the W NCSs.

Abstract

The paper considers a wireless networked control system (WNCS), where a controller sends packets carrying control information to an actuator through a wireless channel to control a physical process for industrial-control applications. In most of the existing work on WNCSs, the packet length for transmission is fixed. However, from the channel-encoding theory, if a message is encoded into a longer codeword, its reliability is improved at the expense of longer delay. Both delay and reliability have great impact on the control performance. Such a fundamental delay-reliability tradeoff has rarely been considered in WNCSs. In this paper, we propose a novel WNCS, where the controller adaptively changes the packet length for control based on the current status of the physical process. We formulate a decision-making problem and find the optimal variable-length packet-transmission policy for minimizing the long-term average cost of the WNCSs. We derive a necessary and sufficient condition on the existence of the optimal policy in terms of the transmission reliabilities with different packet lengths and the control system parameter.

Wireless Feedback Control with Variable Packet Length for Industrial IoT

TL;DR

This letter proposes a novel WNCS, where the controller adaptively changes the packet length for control based on the current status of the physical process, and formulate a decision-making problem and finds the optimal variable-length packet-transmission policy for minimizing the long-term average cost of the W NCSs.

Abstract

The paper considers a wireless networked control system (WNCS), where a controller sends packets carrying control information to an actuator through a wireless channel to control a physical process for industrial-control applications. In most of the existing work on WNCSs, the packet length for transmission is fixed. However, from the channel-encoding theory, if a message is encoded into a longer codeword, its reliability is improved at the expense of longer delay. Both delay and reliability have great impact on the control performance. Such a fundamental delay-reliability tradeoff has rarely been considered in WNCSs. In this paper, we propose a novel WNCS, where the controller adaptively changes the packet length for control based on the current status of the physical process. We formulate a decision-making problem and find the optimal variable-length packet-transmission policy for minimizing the long-term average cost of the WNCSs. We derive a necessary and sufficient condition on the existence of the optimal policy in terms of the transmission reliabilities with different packet lengths and the control system parameter.

Paper Structure

This paper contains 13 sections, 2 theorems, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Controller-Side Operation
  4. Actuator-Side Operation
  5. Control with Variable-Length Packets
  6. Problem Formulation
  7. Semi-MDP Solution
  8. Practical Implementation Issues of Variable-Length Policy
  9. Stability Condition of the Control System
  10. Fixed-Length Packet Transmission Policy
  11. Variable-Length Packet Transmission Policy
  12. Numerical Results
  13. Conclusions

Key Result

Theorem 1

Consider the control system described by system_model-u. Let $(\mathbf{A},\mathbf{\sqrt{R}})$ be controllable and let $(\mathbf{A},\mathbf{\sqrt{Q}})$ be observable.$\sqrt{\mathbf{R}}$ and $\sqrt{\mathbf{Q}}$ are the square roots of the positive definite matrices $\mathbf{R}$ and $\mathbf{Q}$, respe where $\rho(\mathbf{A})$ is the spectral radius of the matrix $\mathbf{A}$.

Figures (3)

  • Figure 1: Variable-length packet transmission policy.
  • Figure 2: The optimal variable-length packet transmission policies within different truncated state spaces.
  • Figure 3: The average cost of fixed-length packet-transmission policy versus the packet length, and the average costs of optimal variable-length policy.

Theorems & Definitions (6)

  • Theorem 1: Fixed-length scenario
  • proof
  • Remark 1
  • Theorem 2: Variable-length scenario
  • proof
  • Remark 2