Adaptive Fuzzy Control With Global Stability Guarantees for Unknown Strict-Feedback Systems Using Novel Integral Barrier Lyapunov Functions

In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated with particular emphasis on global stability. The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determine a priori the compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the ``explosion of complexity'' issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

Automated summary

This article investigates adaptive fuzzy tracking control for uncertain strict-feedback systems with unknown nonlinearities, emphasizing global stability. The proposed control scheme integrates barrier Lyapunov functions with fuzzy approximation and backstepping techniques, introducing novel integral BLFs to overcome design difficulties and guarantee fuzzy approximation validity. The developed controller ensures global stability without prior information of system nonlinearities and prevents the "explosion of complexity" issue.