In this article, approximation model-based control and neural networks-based adaptive control are investigated for obtaining the solution to the motion tracking of a piezoelectric nanopositioning system, respectively. In order to reduce the effect of unknown hysteresis nonlinearity, a disturbance observer is introduced to estimate it. By considering nominal parts of an unknown piezoelectric nanopositioning system, approximation model-based control is obtained. The unknown parts corresponding to nominal parts are dealt with by the online learning ability of neural networks, and an adaptive neural network control is proposed to improve control accuracy. Compared with existing works, a great benefit of the proposed control method is that the neural networks-based learning algorithm is developed to deal with uncertainty of a piezoelectric nanopositioning system in an online way such that the closed-loop system can be governed automatically, obtaining satisfactory motion tracking. With Lyapunov stability theory, it is proved that all error signals are semiglobally uniformly ultimately bounded. Experiment is carried out to verify the effectiveness of the proposed control.

中文翻译：

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压电纳米定位系统的基于神经网络的学习控制

本文研究了基于逼近模型的控制和基于神经网络的自适应控制，以分别获得压电纳米定位系统运动跟踪的解决方案。为了减少未知磁滞非线性的影响，引入了扰动观测器对其进行估计。通过考虑未知压电纳米定位系统的标称零件，可以获得基于近似模型的控制。通过神经网络的在线学习能力来处理与名义零件相对应的未知零件，并提出了一种自适应神经网络控制方法，以提高控制精度。与现有作品相比 所提出的控制方法的一大好处是，开发了基于神经网络的学习算法，以在线方式处理压电纳米定位系统的不确定性，从而可以自动控制闭环系统，从而获得令人满意的运动跟踪。利用李雅普诺夫稳定性理论，证明了所有误差信号都是半全局一致的最终有界的。进行实验以验证所提出控制的有效性。