Fault estimation for a class of nonlinear time-variant systems through a Krein space–based approach

Abstract

This paper studies the [Formula: see text] fault estimation problem for a class of discrete-time nonlinear systems subject to time-variant coefficient matrices, online available input, and exogenous disturbances. By assuming that the concerned nonlinearity is continuously differentiable and by using Taylor series expansions, the dynamic system is transferred as a linear time-variant system with modeling uncertainties. A non-conservative but nominal system and its corresponding [Formula: see text] indefinite quadratic performance function are, respectively, given in place of the transferred uncertain system and the conventional performance metric, such that the estimation problem is converted as a two-stage optimization issue. By introducing an auxiliary model in Krein space, the so-called orthogonal projection technique is utilized to search an appropriate choice serving as the estimation of the fault signal. A necessary and sufficient condition on the existence of the fault estimator is given, and a recursive algorithm for computing the gain matrix of the estimator is proposed. The addressed method is applied to an indoor robot localization system to show its effectiveness.