Sending the most recent observation is not optimal in networked control: Linear temporal coding and towards the design of a control specific transport protocol

This paper explores diversity of temporal observations in a networked control system or sensor network. We analyze what information should be sent between a sensor and a controller (or estimator) in a networked control system (or sensor network) where the two components are separated by an unreliable, bandwidth limited communication. Packets may be dropped at any time. Given a sensor of limited computational and storage capability restricted to transmitting linear combinations of measurements, we consider what should be transmitted following a packet drop - the most recent observation, the previously dropped observation, or a combination of the two? We show that the common practice of sending only the most recent observation is not optimal. We then derive necessary and sufficient conditions for an optimal linear combination of past and present observations. We address a special case where sensor bandwidth (or sampling rate) is higher than communication bandwidth (or throughput), and deal with the case of multiple dropped packets. These results suggest the design of a transport layer specific to networked control which optimizes packet contents contingent on previous packet loss. Alternatively, one could optimize access between contending sensors for a scarce communication medium. The results could be regarded as network coding across time. Simulations are used to illustrate the theoretical results.