Communication-Computation Trade-Off and Optimal Control Selection in LQG Control

In wireless networked control systems, a common challenge arises in deciding between a remote controller, with higher computational power but delayed information due to wireless communication, and a local onboard controller, with limited computing resources but timely feedback. This letter investigates such a trade-off in the context of the Linear Quadratic Gaussian (LQG) control, focusing on the interplay between computational power and communication delay. We compare two typical controllers: a local controller operating at a coarse control rate and a remote controller utilizing a finer control rate but experiencing network delay. A formal analytical framework is proposed to quantify the impact of network delay on the LQG cost and computation resources. We show that there exists a critical communication delay above which the more powerful remote controller is no more convenient with respect to the simpler local controller, providing a guideline for controller selection in varying network conditions with fixed computing resource configurations. Our approach provides a lightweight, interpretable selection rule based on the communication-computation trade-off. Simulation results validate the effectiveness of our theoretical insights.