The scope of this research is a problem of parameters identification of a linear time-invariant plant, which (1) input signal is not frequency-rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above-stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least-squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above-mentioned properties are mathematically proved and demonstrated via simulation experiments.

中文翻译：

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提供模型参数指数收敛的稳健方法解决线性时不变设备识别问题

本研究的范围是线性时不变设备的参数识别问题，该问题（1）输入信号不是频率丰富的，（2）受到初始条件和外部干扰的影响。记忆回归器扩展 (MRE) 方案，其中使用专门导出的微分方程作为滤波器，用于解决上述问题。这样的过滤器允许我们获得有界回归量值，满足初始激励（IE）的条件。使用 MRE 方案，使用带有遗忘因子的递归最小二乘法来推导适应律。已为所提出的方法证明了以下性质。如果满足IE条件，则：(1) 辨识的参数误差是有界的，并以指数方式收敛到零（如果没有外部扰动）或收敛到一个具有可调速率的集合（在它们的情况下）， (2) 参数自适应速率是一个有限值. 上述性质通过数学模拟实验得到证明和证明。