The paper considers a block-oriented nonlinear Hammerstein system that consists of a linear block with real-valued time-varying unknown coefficients and a pure time delay, preceded by the static nonlinearity. The joint tracking of linear block coefficients and the time delay while processing observation samples is under consideration. The difficulty of the tracking process consists in the initial nonconvexity of the objective function to be minimized, in respect of the time delay. To obtain current estimates of the true coefficients and the time delay it is necessary to overcome the multiextremality of the objective function. A global optimization problem could be solved by changing a form of the nonconvex objective function into a convex one. The optimization problem has been subdivided into two problems that are analyzed in this article, as well. The first one consists of removal of the objective function multiextremality in respect of the time delay, while hunting for the global extremum. Therefore, the well-known approach based on the method of corrective operators, which is used to transform the multiextremal criterion into a unimodal function for the nonstationary Wiener system, is developed here for the Hammerstein one. The other problem consists of the applicability of unified adaptive algorithms, used for Wiener systems in the case of Hammerstein systems. The recursive parametric identification technique, based on the adaptive algorithm procedures, is developed here for the nonstationary block-oriented Hammerstein systems, too. The applicability of algorithms is supported by various simulation tests solved by computer for distinct inputs and for two static nonlinearities.

中文翻译：

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非平稳线性系统的联合跟踪系数和时间延迟，之前是静态非线性

该论文考虑了一个面向块的非线性 Hammerstein 系统，该系统由一个具有实值时变未知系数和纯时间延迟的线性块组成，前面是静态非线性。线性块系数的联合跟踪和处理观察样本时的时间延迟正在考虑中。跟踪过程的困难在于要最小化目标函数的初始非凸性，就时间延迟而言。为了获得真实系数和时间延迟的当前估计值，必须克服目标函数的多重极值性。全局优化问题可以通过将非凸目标函数的一种形式变为凸目标函数来解决。优化问题也被细分为本文分析的两个问题。第一个包括去除关于时间延迟的目标函数多极值，同时寻找全局极值。因此，这里为 Hammerstein 系统开发了一种众所周知的基于校正算子方法的方法，该方法用于将多极值准则转换为非平稳 Wiener 系统的单峰函数。另一个问题包括统一自适应算法的适用性，在 Hammerstein 系统的情况下用于 Wiener 系统。递归参数识别技术，基于自适应算法程序，这里也为非平稳块导向 Hammerstein 系统开发。算法的适用性得到了计算机针对不同输入和两个静态非线性求解的各种模拟测试的支持。