Attitude stabilization of a rigid body with measurement noise and time-delayed feedback

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-03 DOI:10.1016/j.cnsns.2025.108887

Manmohan Sharma , Ramalingam Sakthivel

{"title":"Attitude stabilization of a rigid body with measurement noise and time-delayed feedback","authors":"Manmohan Sharma , Ramalingam Sakthivel","doi":"10.1016/j.cnsns.2025.108887","DOIUrl":null,"url":null,"abstract":"<div><div>The article presents a method to stabilize the attitude of a rigid body in the presence of measurement noise and delayed feedback on the nonlinear manifold <span><math><mrow><mi>T</mi><mi>S</mi><mi>O</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. It is assumed that the measurements of angular velocity and attitude are influenced by a bounded white noise process. The analysis of such a system cannot be done with ordinary differential equations, but stochastic functional differential equations should be invoked. Moreover, for the stability analysis, It <span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>’s formula has been derived on <span><math><mrow><mi>T</mi><mi>S</mi><mi>O</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> since the commonly used It <span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>’s formula cannot be used on <span><math><mrow><mi>T</mi><mi>S</mi><mi>O</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. Finally, Lyapunov Razumikhin’s theorem has been used to derive a condition for stabilizing attitude with delayed feedback. Simulation and comparison results have been presented to validate the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108887"},"PeriodicalIF":3.4000,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425002989","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

The article presents a method to stabilize the attitude of a rigid body in the presence of measurement noise and delayed feedback on the nonlinear manifold

T S O (3)

. It is assumed that the measurements of angular velocity and attitude are influenced by a bounded white noise process. The analysis of such a system cannot be done with ordinary differential equations, but stochastic functional differential equations should be invoked. Moreover, for the stability analysis, It

\hat{o}

’s formula has been derived on

T S O (3)

since the commonly used It

\hat{o}

’s formula cannot be used on

T S O (3)

. Finally, Lyapunov Razumikhin’s theorem has been used to derive a condition for stabilizing attitude with delayed feedback. Simulation and comparison results have been presented to validate the theoretical findings.

查看原文本刊更多论文

具有测量噪声和时滞反馈的刚体姿态稳定

本文提出了一种在非线性流形TSO(3)存在测量噪声和延迟反馈的情况下稳定刚体姿态的方法。假设角速度和姿态的测量受到有界白噪声过程的影响。这种系统的分析不能用常微分方程来完成，而应使用随机泛函微分方程。此外，对于稳定性分析，由于通常使用的It o´s公式不能用于TSO(3)，因此在TSO(3)上推导了It o´s公式。最后，利用Lyapunov Razumikhin定理导出了时滞反馈下姿态稳定的一个条件。仿真和对比结果验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.