Linear systems are a widely used model for the control tasks of modern cyber physical systems around their stationary state(s), e.g., smart grids, remote health applications, and autonomous driving systems. Specifically, each sensor first compresses its own measurement and then sends it to the controller. Due to the inevitable random communication delay, the controller needs to decide how to fuse the received information to compute the desired control action. Suppose a fusion center has received several measurements over time. One common belief is that the control decision should be made solely based on the latest measurement of each sensor while ignoring the older/stale measurements from the same sensor. This work shows that while such a strategy is optimal in a single-sensor environment, it can be strictly suboptimal for a multi-sensor system. Namely, if one properly fuses both the latest and outdated measurements from each of the sensors, one can strictly improve the underlying control system performance. The numerical evaluation shows that even at a very low communication rate of 8 bits per measurement per sensor, the proposed scheme achieves a state variance of only 5% away from the best possible achievable L2 norm. It is 15% better than the MMSE fusion scheme using exclusively the freshest measurements (while discarding outdated ones).
Rate-stability tradeoff, random delay, information fusion, age of information, linear control systems
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