Adaptive fixed-time tracking control for uncertain nonlinear systems with unknown control coefficients and prescribed performance

Abstract

This paper delves into the problem of fixed-time neural network adaptive prescribed performance control for a category of nonstrict-feedback systems with time-varying unknown control coefficients (UCCs). Firstly, two key technical lemmas are proposed. One is to put forward a novel fixed-time stability lemma with a more precise upper-bound estimate of the settling time. The other is to present a new lemma based on a category of type-B Nussbaum functions (TBNFs), which can effectively address the time-varying UCCs in the systems. Secondly, neural networks are employed to approach the uncertain nonlinear terms, and a fixed-time performance function and a nonlinear shifting function are constructed to eliminate the restriction of tracking error in terms of initial condition. Then, to overcome the singularity problem, the switched virtual controllers are designed with the help of the novel fixed-time stability lemma and dynamic surface control technique. It turns out that the tracking error converges to a predefined asymmetric constraint region within a fixed time and the closed-loop system is practically fixed-time stable. Finally, a numerical example and a mass-spring-damper system are provided to verify the effectiveness of the presented design method.