  Real-time remote control over wireless is an important-yet-challenging
application in 5G and beyond due to its mission-critical nature under limited
communication resources. Current solutions hinge on not only utilizing
ultra-reliable and low-latency communication (URLLC) links but also predicting
future states, which may consume enormous communication resources and struggle
with a short prediction time horizon. To fill this void, in this article we
propose a novel two-way Koopman autoencoder (AE) approach wherein: 1) a sensing
Koopman AE learns to understand the temporal state dynamics and predicts
missing packets from a sensor to its remote controller; and 2) a controlling
Koopman AE learns to understand the temporal action dynamics and predicts
missing packets from the controller to an actuator co-located with the sensor.
Specifically, each Koopman AE aims to learn the Koopman operator in the hidden
layers while the encoder of the AE aims to project the non-linear dynamics onto
a lifted subspace, which is reverted into the original non-linear dynamics by
the decoder of the AE. The Koopman operator describes the linearized temporal
dynamics, enabling long-term future prediction and coping with missing packets
and closed-form optimal control in the lifted subspace. Simulation results
corroborate that the proposed approach achieves a 38x lower mean squared
control error at 0 dBm signal-to-noise ratio (SNR) than the non-predictive
baseline.
