In closed-loop wireless control systems, the state-of-the-art approach prescribes that a controller receives by wireless communications the individual sensor measurements, and then sends the computed control signal to the actuators. We propose an over-the-air controller scheme where all sensors attached to the plant simultaneously transmit scaled sensing signals directly to the actuator; then the feedback control signal is computed partially over the air and partially by a scaling operation at the actuator. Such over-the-air controller essentially adopts the over-the-air computation concept to compute the control signal for closed-loop wireless control systems. In contrast to the state-of-the-art sensor-to-controller and controller-to-actuator communication approach, the over-the-air controller exploits the superposition properties of multiple-access wireless channels to complete the communication and computation of a large number of sensing signals in a single communication resource unit. Therefore, the proposed scheme can obtain significant benefits in terms of low actuation delay and low wireless resource utilization by a simple network architecture that does not require a dedicated controller. Numerical results show that our proposed over-the-air controller achieves a huge widening of the stability region in terms of sampling time and delay, and a significant reduction of the computation error of the control signal.
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