Fuzzy Adaptive Containment Control for Nonlinear Nonaffine Pure-Feedback Multiagent Systems

Abstract

This article addresses the containment control problem of multiagent systems under directed topologies, where the model of each agent is an unknown nonlinear nonaffine pure-feedback dynamic, and at the same time, the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then, the fuzzy logic systems and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme.