This article settles consensus of nonlinearly parameterized multi-agent systems with periodic disturbances by using matrix theory, adaptive control, neural networks and fourier series expansion. Firstly, uncertain nonlinear dynamics with unmeasurable periodic input disturbances are constructed and described by using fourier series expansion and neural networks. Secondly, a novel distributed control protocol based on adaptive control method and matrix theory is designed to make the second-order closed-loop systems asymptotically stable. Thirdly, another new distributed control protocol based on the above consensus protocol is designed to make the closed-loop system with unknown control directions asymptotically stable. Finally, the correctness of the two control protocols is verified by three simulation examples.

本文通过使用矩阵理论、自适应控制、神经网络和傅里叶级数展开来解决具有周期性扰动的非线性参数化多智能体系统的共识。首先，利用傅里叶级数展开和神经网络构建和描述具有不可测周期性输入扰动的不确定非线性动力学。其次，设计了一种基于自适应控制方法和矩阵理论的新型分布式控制协议，使二阶闭环系统渐近稳定。第三，在上述共识协议的基础上，设计了另一种新的分布式控制协议，使控制方向未知的闭环系统渐近稳定。最后通过三个仿真实例验证了两种控制协议的正确性。