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Distributed Channel Access for Control Over Unknown Memoryless Communication Channels

Tahmoores Farjam, Henk Wymeersch, Themistoklis Charalambous

TL;DR

This work proposes a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems by utilizing timers for prioritizing channel access with respect to a local cost which is derived by transforming the control objective cost to a form that allows its local computation.

Abstract

We consider the distributed channel access problem for a system consisting of multiple control subsystems that close their loop over a shared wireless network. We propose a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems. This is achieved by utilizing timers for prioritizing channel access with respect to a local cost which we derive by transforming the control objective cost to a form that allows its local computation. This property is then exploited for developing our distributed deterministic channel access scheme. A framework to verify the stability of the system under the resulting scheme is then proposed. Next, we consider a practical scenario in which the channel statistics are unknown. We propose learning algorithms for learning the parameters of imperfect communication links for estimating the channel quality and, hence, define the local cost as a function of this estimation and control performance. We establish that our learning approach results in collision-free channel access. The behavior of the overall system is exemplified via a proof-of-concept illustrative example, and the efficacy of this mechanism is evaluated for large-scale networks via simulations.

Distributed Channel Access for Control Over Unknown Memoryless Communication Channels

TL;DR

This work proposes a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems by utilizing timers for prioritizing channel access with respect to a local cost which is derived by transforming the control objective cost to a form that allows its local computation.

Abstract

We consider the distributed channel access problem for a system consisting of multiple control subsystems that close their loop over a shared wireless network. We propose a distributed method for providing deterministic channel access without requiring explicit information exchange between the subsystems. This is achieved by utilizing timers for prioritizing channel access with respect to a local cost which we derive by transforming the control objective cost to a form that allows its local computation. This property is then exploited for developing our distributed deterministic channel access scheme. A framework to verify the stability of the system under the resulting scheme is then proposed. Next, we consider a practical scenario in which the channel statistics are unknown. We propose learning algorithms for learning the parameters of imperfect communication links for estimating the channel quality and, hence, define the local cost as a function of this estimation and control performance. We establish that our learning approach results in collision-free channel access. The behavior of the overall system is exemplified via a proof-of-concept illustrative example, and the efficacy of this mechanism is evaluated for large-scale networks via simulations.

Paper Structure

This paper contains 21 sections, 4 theorems, 59 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. Local Processes and Measurements
  4. Imperfect Communication
  5. Control and Estimation
  6. Cost of Information Loss (CoIL)
  7. Timer-based Mechanism
  8. Distributed Channel Access Mechanism
  9. Timer Setup
  10. Stability Analysis
  11. Channel access over unknown memoryless channels
  12. Problem Statement
  13. A MAB Approach
  14. Distributed Channel Access Algorithm
  15. Numerical Results
  16. ...and 6 more sections

Key Result

Lemma 1

Consider the cost criterion defined in eq:cost. The stage cost at $k$ is given by where $\Gamma_{i,\infty} = L_{i,\infty}^{\hbox{\tiny T}}(B_i^{\hbox{\tiny T}} \Pi_{i,\infty} B_i + R_i)L_{i,\infty}$.

Figures (8)

  • Figure 1: Example of the WNCS layout where $N$ subsystems compete to access a shared wireless channel $j$. $\mathcal{P}_i$ represents the plant of subsystem $i\in\{1,\ldots,N\}$, with $\mathcal{S}_i$, $\mathcal{E}_i$, and $\mathcal{C}_i$ being its sensor, estimator and controller, respectively. Note that the timer is embedded in the smart sensor and determines whether $\hat{x}_{i,k|k}^s$ is transmitted from $\mathcal{S}_i$ to $\mathcal{E}_i$.
  • Figure 2: Two-dimensional Markov chain modeling the evolution of $(t_{1,k},t_{2,k})$ in a WNCS where two subsystems share a single channel. Here, the transition probabilities $\rho_1$, $\rho_2$, and $\rho_3$ correspond to \ref{['eq:Pr1']}, \ref{['eq:Pr2']}, and \ref{['eq:Pr3']}, respectively.
  • Figure 3: Graphical representation of the truncated version of the Markov chain depicted in Fig. \ref{['fig:Markov']}.
  • Figure 4: Convergence analysis of the left hand side \ref{['eq:convres']} by element-wise comparison with the p-series ($\beta=100$, $p=2$) given that $q_1=0.40$ and $q_2=0.44$.
  • Figure 5: Convergence analysis of the left hand side \ref{['eq:convres']} by element-wise comparison with the p-series ($\beta=100$, $p=2$) given that $q_1=0.20$ and $q_2=0.44$.
  • ...and 3 more figures

Theorems & Definitions (14)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3
  • Definition 1: Lyapunov mean square stability Kozin:1969
  • Lemma 3
  • proof
  • ...and 4 more