Global Fixed-Time Stability of General Stochastic Nonlinear Systems

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-08-16 DOI:10.1155/2024/5517265
Liandi Fang, Daohong Zhu, Zhenzhen Long
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引用次数: 0

Abstract

In this article, the fixed-time stabilization issue is investigated for a kind of general p-norm stochastic nonlinear systems. The feature of the considered systems is that all powers are any positive rational numbers, which means this type of systems includes many previously considered systems. Firstly, a higher accurate upper bounded estimation of settling time is given by applying an ingenious variable transformation and the definition of Gamma function, thereby obtaining an improved stochastic fixed-time stability theorem. Then a continuous state-feedback controller is designed for the general p-norm stochastic systems by using the adding a power integrator method, and the designed controller is proved to ensure the fixed-time stability of the considered systems in light of stochastic fixed-time stability theorem. Finally, numerical simulation results of fixed-time stabilizer and finite-time stabilizer indicate the effectiveness of the developed scheme.

Abstract Image

一般随机非线性系统的全局固定时间稳定性
本文研究了一种一般 p-norm 随机非线性系统的固定时间稳定问题。所考虑的系统的特点是所有幂都是任意正有理数,这意味着这类系统包括许多以前考虑过的系统。首先,通过应用巧妙的变量变换和伽马函数的定义,给出了更高精度的沉降时间上限估计,从而得到了改进的随机定时稳定性定理。然后,利用添加功率积分器的方法为一般 p 规范随机系统设计了连续状态反馈控制器,并根据随机定时稳定性定理证明了所设计的控制器能确保所考虑系统的定时稳定性。最后,固定时间稳定器和有限时间稳定器的数值模拟结果表明了所开发方案的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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