Joint State and Fault Estimation of Complex Networks Under Measurement Saturations and Stochastic Nonlinearities

In this paper, the joint state and fault estimation problem is investigated for a class of discrete-time complex networks with measurement saturations and stochastic nonlinearities. The difference between the actual measurement and the saturated measurement is regarded as an unknown input and the system is thus re-organized as a singular system. An appropriate estimator is designed for each node which aims to estimate the system states and the loss of the actuator effectiveness simultaneously. In the presence of measurement saturations and stochastic nonlinearities, upper bounds of the error covariances of the fault estimates are recursively obtained and then minimized. Sufficient conditions are proposed to guarantee the existence, unbiasedness, and boundeness of the developed estimator. Our developed estimator design algorithm is distributed because it depends only on the local information and the information from the neighboring nodes, thereby avoiding the usage of a center estimator. Finally, simulation results are presented to show the performance of the proposed strategy in simultaneously estimating the states and faults.