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Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems. (English) Zbl 1309.93155
Summary: This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an \(H_\infty\)-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon \(H_\infty\) fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati Difference Equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method.

93E10 Estimation and detection in stochastic control theory
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
93B36 \(H^\infty\)-control
Full Text: DOI
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