Krein Space Based $$H_\infty $$ Fault Estimation for Discrete-Time Nonlinear Systems

Abstract

AbstractThis chapter demonstrates a Krein space based finite horizon \(H_\infty \)-filtering method for discrete-time nonlinear systems and, on this basis, handling \(H_\infty \) fault estimation issues for the INS/GPS integrated system by combing it with proportional and multi-integral (PMI) observer scheme. The core idea lies in converting the targeting problem into a minimum of an indefinite quadratic form such that a relationship between nonlinear filter in Hilbert space and nonlinear estimation in Krein space can be established. Then, by using first-order Taylor approximation and Krein space projection, a sufficient and necessary condition for the minimum is derived and a feasible solution of the nonlinear filter can be obtained by recursively computing Riccati recursions. Especially, for fault estimation purpose, a PMI based nonlinear fault estimator is constructed and designed in the framework of \(H_\infty \) filtering. Successful applications of the results in INS/GPS integrated system are demonstrated through experimental studies.