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- W2045173605 abstract "A method is presented for the identification of a nonlinear dynamical system whose input-output map is assumed to be a Volterra series mapping inputs u belonging to $L^2 (I)$ to outputs y in the Sobolev space $H_n^2 (I)$, where I is a compact interval of the real line and n is a nonnegative integer. The input-output relation is denoted by $y(t) = V(u)(t) triangleq V_t (u)$, $t in I$. It is assumed also that a set of test input-output pairs ${ {u_j in L^2 (I),y_j in H_n^2 (I):j = 1, cdots ,m} }$ are provided. Our system identification procedure is based on the construction of a reproducing kernel Hilbert space, namely a symmetric Fock space $F_rho $, for the nonlinear functional $V_t $. The corresponding nonlinear operator V then belongs to a Bochner space $B_n^2 $. We obtain the best estimate $hat V$ of V, based on the input-output data, in the form of a generalized inverse in $B_n^2 $. Both the noncausal and causal versions of $hat V$ are derived. The concept of $varepsilon $-causality, which is weaker than that of causality, is also introduced and motivated, and an $varepsilon $-causal solution to the system identification problem is derived. Finally, the modifications needed to be introduced in the above solutions when the data is noisy are indicated." @default.
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- W2045173605 title "Nonlinear System Identification Based on a Fock Space Framework" @default.
- W2045173605 doi "https://doi.org/10.1137/0321056" @default.
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