Backstepping-based adaptive fuzzy tracking control for pure-feedback nonlinear multi-agent systems

This work developed an adaptive fuzzy tracking control strategy for pure-feedback nonlinear multi-agent systems via backstepping. The relevant unknown functions are addressed by fuzzy logic systems (FLSs), which take into account entirely unknown nonlinearities. The non-affine pure-feedback form is dealt with a Butterworth low-pass filter (BLF), and the converted systems can be used to construct a controller. The implementation of the first-order sliding-mode differentiator overcomes the difficulty of calculation explosion. The backstepping method is applied to design the virtual controller step by step, and the actual controller is designed successfully. Furthermore, through Lyapunov stability theory, the stability of systems is ensured, and that the tracking error is kept to a minimum. Finally, the simulation result shows the validity of the designed control strategy.