This work studies the problem of LQG control when the link between the sensor and the controller relies on a Wi-Fi network. Unfortunately, the communication on a wireless medium is sensitive to noise in the transmission band, which is characterized by the Signal-to-Noise Ratio (SNR). Wi-Fi allows to switch among different bit-rates in real-time thus permitting to trade-off lower loss probabilities for larger latency or vice-versa to achieve better closed-loop performance. To exploit this feature, under a constant SNR scenario, we propose a cross-layer approach where the bit-rate is optimally selected based on a control performance metric (i.e. minimum LQG cost) and a model-based controller is used to compensate for the packet losses. Under time-varying SNR, we additionally propose a (sub-optimal) on-line rate adaptation strategy and we guarantee the closed-loop stability under some mild conditions. Numerical comparisons with emulation-based approaches using TrueTime, a realistic Matlab-based Wi-Fi simulator, are included to show the benefits of the adaptive approach under time-varying SNR scenarios.

这项工作研究了当传感器和控制器之间的链接依赖于Wi-Fi网络时的LQG控制问题。不幸的是，无线介质上的通信对传输带中的噪声敏感，其特征在于信噪比（SNR）。Wi-Fi允许实时在不同的比特率之间进行切换，因此可以权衡较低的丢失概率以获得更大的延迟，反之亦然，以实现更好的闭环性能。为了利用此功能，在恒定SNR情况下，我们提出了一种跨层方法，其中根据控制性能指标（即最小LQG成本）最优选择比特率，并使用基于模型的控制器来补偿数据包丢失。在SNR随时间变化的情况下，我们还提出了（次优）在线速率自适应策略，并保证在某些温和条件下的闭环稳定性。包括使用TrueTime（基于Matlab的真实Wi-Fi模拟器）与基于仿真方法的数值比较，以显示自适应方法在时变SNR场景下的优势。