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One-shot set-membership identification of generalized Hammerstein-Wiener systems. (English) Zbl 1447.93059
Nonlinear dynamic systems identification is one of the most interesting fields of contemporary industrial mathematics. It origins from the classic Weierstrass approximation theorem and Frénchet’s results that a continuous real functional defined on a compact set of real continuous functions could be approximated by the sum of a finite number of the Volterra functional series’ terms. Here readers may refer to the monograph by D. Sidorov [Integral dynamical models. Singularities, signals and control. Hackensack, NJ: World Scientific (2015; Zbl 1311.45012)] and its bibliography. The Hammerstein and Wiener models can be considered as special kinds of nonlinear dynamic systems where the nonlinear block is static and follows (or followed by) a linear system. The main result of this manuscript is the new approach to set-membership identification of Wiener systems with polynomial output nonlinearity by reduction to the nonconvex optimization problem attacked using the sparsity structure of the nonconvex problem. The authors claim that the proposed approach allows estimating the parameters of both the linear and the nonlinear systems during the single active experiment. Moreover, it is claimed that there are no imposed constraints on the input/output signals types.
MSC:
93B30 System identification
93C10 Nonlinear systems in control theory
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