Channel Access Strategies for Control-Communication Co-Designed Networks

TL;DR

A statistical analysis of control performance is followed by a Thompson sampling-based algorithm to optimize the ALOHA parameter, achieving sub-linear regret and showing how the ALOHA parameter influences control performance and transmission success in both system types.

Abstract

We develop a framework for communication-control co-design in a wireless networked control system with multiple geographically separated controllers and controlled systems, modeled via a Poisson point process. Each controlled system consists of an actuator, plant, and sensor. Controllers receive state estimates from sensors and design control inputs, which are sent to actuators over a shared wireless channel, causing interference. Our co-design includes control strategies at the controller based on sensor measurements and transmission acknowledgments from the actuators for both rested and restless systems - systems with and without state feedback, respectively. In the restless system, controllability depends on consecutive successful transmissions, while in the rested system, it depends on total successful transmissions. We use both classical and block ALOHA protocols for channel access, optimizing access based on sensor data and acknowledgments. A statistical analysis of control performance is followed by a Thompson sampling-based algorithm to optimize the ALOHA parameter, achieving sub-linear regret. We show how the ALOHA parameter influences control performance and transmission success in both system types.

Figures (5)

• Figure 1: Illustration of the Poisson network of controller-controlled system pairs. Here, the actuators receive the control input from the corresponding controller via a shared link, whereas the sensors send their observations to the controller via a dedicated link.
• Figure 2: Probability of block controllability for the rested and restless systems with block or classical ALOHA channel access schemes. Here $T = 20$, $v = 4$, and $\lambda = 5e-3$ m$^{-2}$.
• Figure 3: Comparison of block controllability probability of restless system with $v = 5$ in a block length of $T = 20$ and the relative selection of the ALOHA parameters by the block TS framework in $K = 5000$ blocks.
• Figure 4: Comparison of the meta distribution $\mathcal{M}_{\rm RD,cls}(v, \beta=0.9)$ of rested system with classical ALOHA and the relative selection of the classical ALOHA parameter by the TS framework in $K=5000$ slots.
• Figure 5: Regret for the restless system for different values of $v$ and $\lambda$.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Theorem 1
• proof