Chapter 11 - Robust State and Fault Estimation for Linear Descriptor and Nonlinear Stochastic Systems With Disturbances

Abstract

This chapter considers the problem of simultaneously estimating the state and the fault of linear, descriptor, and nonlinear descriptor discrete-time stochastic systems with arbitrary unknown disturbances via unknown input filtering. It is shown that, within this new filtering approach, the optimal robust state and fault estimation can be simultaneously achieved through the previously proposed robust two-stage Kalman filter. A restricted system reformation (RSR) model is first obtained for the considered linear system with faults and unknown disturbances, and then a robust state and fault estimator (RSFE) is designed based on the RSR representation. Afterward, the descriptor stochastic system is transformed into an equivalent standard augmented state system with unknown inputs, then it can be shown that the proposed RSFE is ready to be applied to yield the optimal RSFE for descriptor systems, which is able to detect and estimate the actuator and sensor faults while decoupling the unknown disturbances. The design conditions for this proposed filter are also derived. In the end, the proposed linear unknown input filtering method is extended to solve the RSFE design problem for nonlinear descriptor systems with unknown disturbances by using the state-dependent coefficient factorization method. In the sequel, a novel simultaneous fault and state estimator is proposed to yield the optimal robust state and actuator and/or sensor faults in the presence of unknown disturbances. Finally, numerical examples are exploited to show the effectiveness of the proposed various estimators compared with other existing filters in the literature.