In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.

中文翻译：

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基于梯度下降-Barzilai Borwein 的未知动力学非线性系统神经网络跟踪控制

在本文中，针对一类具有未知漂移函数和控制输入增益函数的非线性系统，提出了一种组合梯度下降-Barzilai Borwein (GD-BB) 算法和径向基函数神经网络 (RBFNN) 输出跟踪控制策略。在这种方法中，神经网络 (NN) 用于直接逼近控制器。所提出策略的主要优点如下：首先，不仅神经网络参数，如权重、中心和宽度，而且神经网络参数更新规律的学习率都通过所提出的基于 Barzilai 的学习算法在线更新。鲍温技术；其次，可以进一步简化控制器的设计过程，大大减少需要整定的控制器参数。对闭环系统的稳定性进行了理论分析。此外，还对数值离散时间系统和倒立摆系统进行了仿真，以验证所提出的控制策略。