This paper focuses on a problem of adaptive fuzzy containment control for nonlinear multi-agent systems with input delay. Through the Pade approximation and intermediate variable, the positive constant delays of nonlinear systems inputs are transferred to the coefficients of the next dynamic equation. The phenomenon of “complexity explosion” in traditional backstepping control technique is avoided by introducing first-order filters, in which a new variable replaces the derivative of the virtual controller. In addition, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions of nonlinear multi-agent systems. No matter what the order of the nonlinear multi-agent systems is, only two adaptive laws need to be designed in the adaptive fuzzy containment controller design process for each follower. Using the proposed control method, all followers can converge to the convex hull established by the leaders, and the closed-loop system is stable. The simulation results can further illustrate the effectiveness of the proposed control method.

本文针对具有输入延迟的非线性多智能体系统的自适应模糊包含控制问题。通过帕德逼近和中间变量，非线性系统输入的正恒定延迟被传递到下一个动力学方程的系数。通过引入一阶滤波器来避免传统反步控制技术中的“复杂性爆炸”现象，在该滤波器中，一个新变量替代了虚拟控制器的导数。此外，模糊逻辑系统（FLS）用于逼近非线性多主体系统的未知非线性函数。无论非线性多智能体系统的顺序是什么，在每个跟随者的自适应模糊约束控制器设计过程中只需设计两个自适应定律。使用提出的控制方法，所有跟随者都可以收敛到由领导者建立的凸包，并且闭环系统是稳定的。仿真结果可以进一步说明所提控制方法的有效性。