Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay

TLDR

The paper develops an adaptive fuzzy tracking control scheme for nonlinear strict‑feedback systems with input delay and output constraints, aiming to achieve semiglobal uniform ultimate boundedness and a tracking error that can be tightened around the origin. The scheme compensates input delay via a Pade approximation, enforces output constraints with a barrier Lyapunov function, and updates adaptive parameters online using the norm of the membership function vector. Stability of the closed‑loop system is proven, and simulation results confirm the controller’s effectiveness.

Abstract

This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.