Narendra K S, Mukhopadhyay S
Center for Syst. Sci., Yale Univ., New Haven, CT.
IEEE Trans Neural Netw. 1997;8(3):475-85. doi: 10.1109/72.572089.
The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.
NARMA模型精确地表示了有限维非线性离散时间动态系统在平衡状态邻域内的输入输出行为。然而，由于它对控制输入的非线性依赖，对于使用神经网络进行自适应控制而言并不方便。因此，为了克服计算复杂性，实现神经控制器时常常采用近似方法。在本文中，我们介绍了两类模型，它们是NARMA模型的近似，并且在控制输入方面是线性的。后一事实极大地简化了控制器的理论分析以及实际实现。大量的仿真研究表明，使用所提出的近似模型设计的神经控制器表现非常出色，并且在许多情况下甚至比使用精确NARMA模型设计的近似控制器还要好。鉴于它们在数学上的易处理性以及在仿真研究中的成功，本文认为这类近似输入输出模型本身值得进行详细研究。
