In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

中文翻译：

---

一类具有未知滞后的非线性系统的自适应采样数据观测器设计

在本文中，基于径向基函数神经网络（RBFNN），研究了一类具有未知Prandtl–Ishlinskii磁滞和未知不匹配干扰的非线性系统的新型自适应采样数据观测器设计。首先，我们研究了一个采样数据非线性系统，并提出了足够的条件，以便最终使采样数据非线性系统均匀受界（UUB）。然后，设计了自适应采样数据观测器以估计非线性系统的未知状态。未知磁滞和未知扰动可通过RBFNN估算。我们还给出了RBFNN权重的学习规律，并基于获得的充分条件和特殊构造的Lyapunov–Krasovskii函数，证明了状态和权重的估计误差为UUB。最后，