This paper deals with two problems: the identification and compensation of hysteresis nonlinearity in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). First, based on gray-box identification techniques, some constraints on the structure and parameters of NARX models are proposed to ensure that the identified models display a key feature of hysteresis. In addition, a more general framework is developed to explain how hysteresis occurs in such models. Second, two strategies to design hysteresis compensators are presented. In one strategy, the compensation law is obtained through simple algebraic manipulations performed on the identified models. In the second strategy, the compensation law is directly identified from the data. Both numerical and experimental results are presented to illustrate the efficiency of the proposed procedures. Also, it has been found that the compensators based on gray-box models outperform the cases with models identified using black-box techniques.

本文涉及两个问题：使用具有外部输入的非线性多项式自回归模型（NARX）来确定和补偿动态系统中的磁滞非线性。首先，基于灰盒识别技术，提出了对NARX模型的结构和参数的一些约束，以确保所识别的模型显示出滞后的关键特征。此外，开发了一个更通用的框架来解释在此类模型中磁滞如何发生。其次，提出了两种设计磁滞补偿器的策略。在一种策略中，补偿律是通过对识别出的模型进行简单的代数运算而获得的。在第二种策略中，直接从数据中识别出补偿定律。数值和实验结果都被用来说明所提出的程序的效率。而且，已经发现，基于灰箱模型的补偿器在使用黑箱技术识别的模型的情况下优于情况。