Predefined-time Stabilization for Nonlinear Stochastic Systems

TL;DR

This paper introduces a control scheme for stochastic systems that guarantees stabilization within a predefined time, improving upon existing finite-time and fixed-time methods by bounding the expected settling time.

Contribution

It proposes a novel stochastic predefined-time stabilization method with Lyapunov results and a state feedback control scheme for nonlinear systems in strict-feedback form.

Findings

The control scheme achieves predefined-time stabilization in stochastic systems.

Lyapunov-type results support the theoretical foundation.

Simulations demonstrate the effectiveness of the proposed method.

Abstract

In this paper, a control scheme for stochastic predefined-time stabilization is proposed, which improves the control effect compared with stochastic finite-time or fixed-time stabilization. The stochastic predefined-time stabilization allows the upper bound of the mathematical expectation of the settling-time function below any given positive value. Some Lyapunov-type results for predefined-time stabilization of general stochastic It\^o systems are presented. Moreover, a state feedback control scheme is designed for a class of stochastic nonlinear systems in strict-feedback form. Two simulation examples are supplied to show the usefulness of the proposed stochastic predefined-time stabilization.