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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.

##### MSC:
 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
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