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

Qin Zhang,Yibin Li,Yueyang Li,Hui Chai

doi:10.1177/0020294019887499

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.

Highlights

When sketching the works on model-based fault diagnosis from 1970s of the last century, different kinds of optimization techniques for robust control have been widely used in this area, which lead to the socalled robust fault diagnosis, for example, see previous works1–6 and the references therein
In contrast with the progress of the aforementioned systems, some works on linear time-variant (LTV) systems appear, especially for linear discrete time-variant (LDTV) systems, which result from the fact that most of the real-world applications or industrial processes are intrinsically time-variant
We aim to propose a novel H‘ fault estimation method for a class of nonlinear time-variant systems, where the shape and amplitude of the fault are provided

Summary

Introduction

When sketching the works on model-based fault diagnosis (including fault detection, fault isolation, and fault estimation) from 1970s of the last century, different kinds of optimization techniques for robust control have been widely used in this area, which lead to the socalled robust fault diagnosis, for example, see previous works and the references therein. The nonlinearity is assumed to be continuously differentiable rather than in the form of state-dependent perturbations, and a dynamic filter acting as the fault estimator is designed through linear estimation methodology in Krein space. We need to build a model in this space with regard to system [9]; find the minimum of Ja, k through linear estimation technique; and select a suitable fkjk such that Jam, kjLk = 0 = Jm, k . 0. To continue, we preliminarily introduce the following model through defining a fictitious output xk + 1 = Hkxk + Bu, kuk + Bf, kfk + Bw, kwk yz, k = Cz, kxk + Dz, kuk + Dfz, kfk + vz, k ð12Þ where h yz, k = yTk fTkjk iT 00 h iT vz, k = vTk vTs, k vTx, k vTu, k. In terms of systems [19]–(22), we have

À g2I 0

Conclusion