Transmission Schedule for Remote State Estimation in CPSs With Two-Hop Networks in Presence of an Eavesdropper

Abstract

In the presence of an eavesdropper, this letter delves into the optimization of the transmission schedule between a sensor and a relay within cyber-physical systems to enhance precise remote state estimation. The system model in question characterizes the plant as a linear time-invariant system, with sensor data being transmitted to the remote estimator through an intelligent relay, while acknowledging the possibility of an eavesdropper intercepting each transmission with a defined probability. Our objective is to decide the optimal timing for both the sensor and the relay to transmit, aiming to minimize the estimation error covariance at the remote estimator, while concurrently seeking to maximize the eavesdropper error covariance. We describe the problem of finding the transmission schedule as a dynamic programming model, and establish structural properties on the optimal schedule, which demonstrate thresholding behaviors in estimation error covariances. Furthermore, in an infinite horizon scenario, it becomes apparent that the expected estimation error covariance at the remote estimator can consistently be controlled, while that of the eavesdropper tends towards infinity for all eavesdropping probabilities strictly less than one.