Remote State Estimation for Cyber-Physical Systems Under Redundancy Transmission Protocol

This article studies a remote state estimation problem for cyber-physical systems (CPSs) under the redundancy transmission protocol (RTP), where a sensor simultaneously transmits local state estimates to a remote estimator via two channels: 1) a random packet dropping channel and 2) a relay network characterized by random packet losses and finite delays. A sufficient and necessary condition for the convergence of the remote estimation error covariance is obtained using a dual-layer Markov chain framework, which shows that the condition is uniquely influenced by the packet dropping rates across the channels and independent of time delays. For a fixed delay, an upper bound on the trace of the mean estimation error covariance is then derived. Compared with the parallel redundancy protocol (PRP) considered in the existing works, the RTP allows both communication channels to fail simultaneously. Finally, a numerical result validates the results.