This paper investigates the design of adaptive tracking neural controllers for first- and second-order nonlinear multi-agent periodic time-varying systems described based on random differential equations, respectively. First, the Fourier series expansion and neural networks are used as the main tools to describe the nonlinear periodic disturbance dynamics of the follower, which transforms the completely nonlinear problem into a partially linearizable problem. Then, the fully distributed adaptive neural controllers are developed based on adaptive estimation, in which new estimation methods are designed to address periodic time-varying perturbations. Furthermore, based on the stochastic Lyapunov stability theory, it is proved that the tracking errors converge asymptotically to a small neighborhood of zero in the sense of mean square. Finally, the efficicency of the proposed controllers is verified using simulations.

本文分别研究了基于随机微分方程描述的一阶和二阶非线性多智能体周期性时变系统的自适应跟踪神经控制器的设计。首先，以傅里叶级数展开和神经网络为主要工具来描述跟随器的非线性周期性扰动动力学，将完全非线性问题转化为部分线性化问题。然后，基于自适应估计开发了完全分布式自适应神经控制器，其中设计了新的估计方法来解决周期性时变扰动。此外，基于随机Lyapunov稳定性理论，证明了跟踪误差在均方意义上渐近收敛到零的一个小邻域。最后，