This paper addresses the problem of adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear time-delayed systems with unknown input saturation and unknown disturbance input. A smooth function is selected to approximate the non-smooth saturation function. By using the command filter method scheme, the well-known problem of the explosion of complexity, which appears in the classical backstepping methods, is avoided. To approximate the unknown nonlinear functions, the radial basis function neural networks (NNs) are deployed. In addition, considering the minimal learning parameter method makes the updating law independent of the number of neural nodes and the order of the system. By using the mean-value theorem, the adaptive NN tracking control law is obtained systematically regardless of pre-known knowledge of input saturation bounds. The proposed control scheme guarantees that the state trajectories of the closed-loop system are semi-global uniformly ultimately bounded in probability and the tracking error finally stays in a small neighborhood around the origin. Eventually, numerical and practical examples show the performance of the proposed controller design.

本文针对一类具有未知输入饱和度和未知干扰输入的非严格反馈随机非线性时滞系统，解决了自适应神经跟踪控制的问题。选择平滑函数以近似非平滑饱和函数。通过使用命令过滤器方法方案，避免了在经典反推方法中出现的众所周知的复杂性爆炸问题。为了近似未知的非线性函数，部署了径向基函数神经网络（NNs）。另外，考虑最小学习参数方法使得更新规律与神经节点的数量和系统的顺序无关。通过使用均值定理，无论输入饱和范围的已知知识如何，系统地获得自适应NN跟踪控制律。所提出的控制方案保证了闭环系统的状态轨迹是半全局一致的，最终最终以概率为界，并且跟踪误差最终保持在原点周围的小范围内。最终，数值和实际例子表明了所提出的控制器设计的性能。