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

• Published in: Measurement and control (London) Vol. 53; no. 3-4; pp. 541 - 550
• Main Authors: Zhang, Qin, Li, Yueyang, Li, Yibin, Chai, Hui
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.03.2020; Sage Publications Ltd; SAGE Publishing
• Subjects: Algorithms; Discrete time systems; H-infinity control; Nonlinear systems; Nonlinearity; Optimization; Series expansion; Taylor series; Krein space; Fault estimation; uncertainty; nonlinearity; time-variant system
• ISSN: 0020-2940; 2051-8730
• DOI: 10.1177/0020294019887499

This paper studies the H ∞ 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 H ∞ 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.