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This paper considers controlled scalar systems relying on a lossy wirelessfeedback channel. In contrast with the existing literature, the focus is not onthe system controller but on the wireless transmit power controller that isimplemented at the system side for reporting the state to the controller. Sucha problem may be of interest, \emph{e.g.}, for the remote control of drones,where communication costs may have to be considered. Determining the powercontrol policy that minimizes the combination of the dynamical system cost andthe wireless transmission energy is shown to be a non-trivial optimizationproblem. It turns out that the recursive structure of the problem can beexploited to determine the optimal power control policy. As illustrated in thenumerical performance analysis, in the scenario of a dynamics withoutperturbations, the optimal power control policy consists in decreasing thetransmit power at the right pace. This allows a significant performance gaincompared to conventional policies such as the full transmit power policy or theopen-loop policy.

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