Energy-efficient transmission policies for the linear quadratic control of scalar systems

TL;DR

This paper develops an optimal energy-efficient power control policy for scalar systems over lossy wireless channels, balancing control performance and transmission energy, with significant improvements over conventional policies.

Contribution

It introduces a novel recursive optimization approach to determine the optimal power control policy for wireless state reporting in scalar control systems.

Findings

Optimal power control decreases transmit power at the right pace.

Significant performance gains over full power and open-loop policies.

Recursive structure simplifies the optimization problem.

Abstract

This paper considers controlled scalar systems relying on a lossy wireless feedback channel. In contrast with the existing literature, the focus is not on the system controller but on the wireless transmit power controller that is implemented at the system side for reporting the state to the controller. Such a problem may be of interest, \emph{e.g.}, for the remote control of drones, where communication costs may have to be considered. Determining the power control policy that minimizes the combination of the dynamical system cost and the wireless transmission energy is shown to be a non-trivial optimization problem. It turns out that the recursive structure of the problem can be exploited to determine the optimal power control policy. As illustrated in the numerical performance analysis, in the scenario of a dynamics without perturbations, the optimal power control policy consists in decreasing the transmit power at the right pace. This allows a significant performance gain compared to conventional policies such as the full transmit power policy or the open-loop policy.