Multiple Receiver Over-the-Air Computation for Wireless Networked Control Systems

TL;DR

This paper introduces a multi-sender, multi-receiver over-the-air computation framework for wireless control systems, enabling direct control signal computation from sensor data without centralized control, optimizing energy and robustness.

Contribution

It presents a novel OAC framework tailored for WNCS with structural constraints, including algorithms for optimal configuration and stability preservation.

Findings

Algorithms converge reliably.

System maintains stability under constraints.

Enhanced robustness and power efficiency.

Abstract

We propose a multi-sender, multi-receiver over-the-air computation (OAC) framework for wireless networked control systems (WNCS) with structural constraints. Our approach enables actuators to directly compute and apply control signals from sensor measurements, eliminating the need for a centralized controller. We use an iterative and convexifying procedure to obtain a control law that is structured with respect to the network topology and minimizes the overall system energy-to-energy gain. Furthermore, we solve a constrained matrix factorization problem to find the optimal OAC configuration with respect to power consumption, robustness, and stability of the WNCS. We prove the convergence of our proposed algorithms and present numerical results that validate our approach to preserve closed-loop stability with robust control performance and constrained power.