Adaptive Fuzzy Tracking Control with Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems

TL;DR

This paper proposes an adaptive fuzzy control method that ensures global prescribed performance with fixed settling time for uncertain nonlinear systems, overcoming initial condition dependencies and singularity issues.

Contribution

It introduces a novel error transformation and a Lyapunov-like energy function to guarantee prescribed-time convergence and boundedness, improving upon existing control strategies.

Findings

Achieves prescribed transient and steady-state performance within fixed time

Removes initial condition dependency for convergence time

Solves the singularity and differential explosion problems in control design

Abstract

Adaptive fuzzy control strategies are established to achieve global prescribed performance with prescribed-time convergence for strict-feedback systems with mismatched uncertainties and unknown nonlinearities. Firstly, to quantify the transient and steady performance constraints of the tracking error, a class of prescribed-time prescribed performance functions are designed, and a novel error transformation function is introduced to remove the initial value constraints and solve the singularity problem in existing works. Secondly, based on dynamic surface control methods, controllers with or without approximating structures are established to guarantee that the tracking error achieves prescribed transient performance and converges into a prescribed bounded set within prescribed time. In particular, the settling time and initial value of the prescribed performance function are completely independent of initial conditions of the tracking error and system parameters, which improves existing results. Moreover, with a novel Lyapunov-like energy function, not only the differential explosion problem frequently occurring in backstepping techniques is solved, but the drawback of the semi-global boundedness of tracking error induced by dynamic surface control can be overcome. The validity and effectiveness of the main results are verified by numerical simulations on practical examples.