Finite-time stability of jump diffusion system and its application in drill-bit tracking control

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems Pub Date : 2025-09-11 DOI:10.1016/j.nahs.2025.101634

Mingyu Wang , Xiaofeng Zong , Xin Chen

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引用次数: 0

Abstract

This paper investigates the finite-time stability of a jump diffusion system with Brownian motion and random jump components. First, we establish a novel Lyapunov-type finite-time stability theorem, which provides a direct way for selecting an appropriate Lyapunov function. It is important to note that our finite-time stability result is significantly distinct from the case involving only Brownian motion. The presence of the jump term disrupts the continuity of the system’s solution paths, thereby introducing additional complexities in the analysis of finite-time stability. Subsequently, we employ this theorem to design a finite-time controller to ensure the finite-time stochastic stability of the tracking error in a drill-bit system. The proposed control strategy guarantees that the tracking error converges to the origin within finite time and remains there thereafter with probability one. Finally, simulation results are presented to validate the effectiveness of the proposed control law in achieving precise drill-bit tracking control.

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跳跃扩散系统的有限时间稳定性及其在钻头跟踪控制中的应用

研究了具有布朗运动和随机跳跃分量的跳跃扩散系统的有限时间稳定性。首先，我们建立了一个新的Lyapunov型有限时间稳定性定理，为选择合适的Lyapunov函数提供了一种直接的方法。值得注意的是，我们的有限时间稳定性结果与只涉及布朗运动的情况有显著不同。跳跃项的存在破坏了系统解路径的连续性，从而在有限时间稳定性分析中引入了额外的复杂性。随后，我们利用这一定理设计了有限时间控制器，以保证钻头系统跟踪误差的有限时间随机稳定性。所提出的控制策略保证了跟踪误差在有限时间内收敛到原点，并以1的概率保持在原点。最后给出仿真结果，验证了所提控制律在实现钻头精确跟踪控制方面的有效性。

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

Nonlinear Analysis-Hybrid Systems AUTOMATION & CONTROL SYSTEMS-MATHEMATICS, APPLIED

CiteScore

8.30

自引率

9.50%

发文量

审稿时长

>12 weeks

期刊介绍： Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.