Adaptive fuzzy containment control for nonlinear multi-agent systems with input delay

Abstract

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.