Joint Parameter and Time-Delay Identification Algorithm and Its Convergence Analysis for Wiener Time-Delay Systems

Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

“…It is emphasized in that “recursive identification methods can be analyzed with theoretical analysis and simulation.” In the case of input delayed by block‐oriented Wiener systems, different aspects, including convergence of the same algorithms, are investigated analytically as well as by simulation . At the same time, there exists a shortage of results based simulation, concerning the joint tracking of the coefficients and the time delay of the nonlinear Wiener system in the case of multiextremal cost function.…”

“…In the case of input delayed by block-oriented Wiener systems, different aspects, including convergence of the same algorithms, are investigated analytically as well as by simulation. [20][21][22] At the same time, there exists a shortage of results based simulation, concerning the joint tracking of the coefficients and the time delay of the nonlinear Wiener system in the case of multiextremal cost function. Therefore, in this paper, we are concentrated on the analysis of Wiener system-based simulation in a low noisy frame, ie, the level of contamination of the signal (x(k), ) by the additive noise N(k) was made insignificant and the process noise v(k) was absent.…”

“…Recently, the "novel" adaptive method of tracking coefficients and time delay has been developed for block-oriented Wiener system. [20][21][22] It is based "on the well-known hierarchical identification principle that consists in decomposing the cost function to be minimized into two cost functions.". Further, "the optimization problem must be considered as an integer optimization problem."…”

“…In fact, the authors simplify the problem undefended, neglecting the initial multiextremality of the cost function. [20][21][22][23][24] Moreover, the authors have proposed such a condition that guarantees the convexity of the cost function, instead of doing something to obtain the necessary convexity for a naturally nonconvex objective function. The author of this paper, after review of the recent scientific production, has not found any published paper, devoted to the joint online tracking coefficients and time delay of Wiener systems, when the mean-squares prediction error criterion is nonconvex, initially.…”

“…Further, “the optimization problem must be considered as an integer optimization problem.” To solve this difficulty, the authors “suggest the use of the rounding property that allows to transform an integer nonlinear optimization problem into a continuous relaxation problem if the cost function is convex.” It is obvious that, in the opposite case, any local optimization procedure will fail accessing a nearest minimum in respect of the time delay. In fact, the authors simplify the problem undefended, neglecting the initial multiextremality of the cost function . Moreover, the authors have proposed such a condition that guarantees the convexity of the cost function, instead of doing something to obtain the necessary convexity for a naturally nonconvex objective function.…”