Fast finite-time control for a class of stochastic low-order nonlinear system with uncertainties

Abstract

This work explores the challenge of adaptive fast finite-time control for stochastic low-order nonlinear systems with uncertainties. It introduces an improved practical finite-time criterion that aims to achieve accelerated convergence. The criterion aims to extend to a larger range of stochastic nonlinear systems, accommodating state uncertainties and integrating Lyapunov functions with varying powers to ensure rapid convergence in the presence of uncertainties. The entire control design approach is based on the backstepping method. Specifically, fuzzy logic systems are employed in the recursive design of controllers and adaptive laws to address complex uncertain terms. Additionally, the desired magnitude target powers of the Lyapunov function in the criterion are effectively obtained by a clever overlapping selection of parameters. Finally, this study demonstrates the practical finite-time stability of stochastic low-order uncertain nonlinear systems and validates the effectiveness of the proposed approach through simulation example, highlighting its ability to achieve fast convergence.