Identification of the nonlinear decreasing system, represented by Volterra polynomial with the separable kernels (Q2715831)

The considered nonlinear decreasing system has the form NEWLINE\[NEWLINE\varphi(x)= \sum^n_{i=1} p_i C^{-1}_i \varphi^i_1(x),\quad \varphi(a)= 0,NEWLINE\]NEWLINE where NEWLINE\[NEWLINE\varphi_1(x)= \int^a_x W(x,y) f(y) dy,\quad 0\leq x\leq a,NEWLINE\]NEWLINE NEWLINE\[NEWLINEC_1= 1,\quad C_i= \int^a_0 \varphi^i_1(x) dx,\quad i= 2,\dots, n,NEWLINE\]NEWLINE NEWLINE\[NEWLINEp_i\geq 0,\quad \sum^n_{i=1} p_i= 1.NEWLINE\]NEWLINE In the identification problem \(f(x)\) is given, and the parameters \(p_i\) and the distribution density \(W(x,y)\) are unknown (\(W(x,y)\geq 0\), \(\int^y_0 W(x,y) dx= 1\)).NEWLINENEWLINENEWLINEA theorem of uniqueness of the solution is proved. The problem of nonlinear identification of a decreasing system is reduced to the problem of quasilinear identification. The set problem of ``the black box'' identification is solved using projective methods, which leads to the solution of nonlinear algebraic equations. The author mentions the use of computers, but there is no example in this paper.