Almost Sure Distributed Robust Observer With Unknown Inputs

In this paper, we deal with the distributed state estimation problem for target systems with unknown inputs, where the communication channels are affected by disturbances. During the communication process, the communication disturbances are relatively small most of the time, but occasionally large communication disturbances can occur. First, this communication disturbance is modeled as a mixed disturbance: stochastic noise and impulsive disturbance, where stochastic noise stands for relatively small communication disturbance most of the time, and impulsive disturbance stands for occasionally large communication disturbance. In addition, the occurrences of impulses follow a Poisson process. Then, a distributed unknown input observer (DUIO) under mixed disturbance is proposed. The sample path behavior of DUIO is analyzed, and sufficient conditions for the existence of the almost sure DUIO are presented, by graph theory and stochastic analysis. Finally, the validity of the designed almost sure DUIO is confirmed by numerical simulations.