Event-Based Control for Synchronization of Stochastic Linear Systems with Application to Distributed Estimation

Abstract: This paper studies the synchronization of stochastic linear systems which are subject to a general class of noises, in the sense that the noises are bounded in covariance but might be correlated with the states of agents and among each other. We propose an event-based control protocol for achieving the synchronization among agents in the mean square sense and theoretically analyze the performance of it by using a stochastic Lyapunov function, where the stability of $c$-martingales is particularly developed to handle the challenges brought by the general model of noises and the event-triggering mechanism. The proposed event-based synchronization algorithm is then applied to solve the problem of distributed estimation in sensor network. Specifically, by losslessly decomposing the optimal Kalman filter, it is shown that the problem of distributed estimation can be resolved by using the algorithms designed for achieving the synchronization of stochastic linear systems. As such, an event-based distributed estimation algorithm is developed, where each sensor performs local filtering solely using its own measurement, together with the proposed event-based synchronization algorithm to fuse the local estimates of neighboring nodes. With the reduced communication frequency, the designed estimator is proved to be stable under the minimal requirements of network connectivity and collective system observability.