SNR-triggered Communication Rate for LQG Control over Wi-Fi

In this work we address the problem of LQG control where the communication between the sensor and the controller/actuator is performed via Wi-Fi, We exploit one feature of Wi-Fi (standard IEEE 802.11) which gives the ability to switch among different data-rates in real-time: a lower transmission rate provides a lower packet loss probability at a price of a larger sampling period. As a matter of fact, it is not obvious how to select the optimal rate from a control perspective. Nevertheless, the packet error probability as a function of the perceived SNR can be obtained either analytically or empirically. Based on these curves, we determine the optimal rate and the optimal LQG controller for any fixed SNR. In a scenario with a time-varying SNR, we also propose a rate adaptation strategy which is triggered by the measured SNR. Numerical simulations and comparisons with current literature are included to show the benefits of our approach.