为二维马尔科夫跳跃罗塞系统及其H∞控制改进的跳跃模型
IEEE transactions on cybernetics
|August 19, 2025
概括
本研究介绍了一种改进的二维马尔科夫跳跃系统 (MJS) 模型,使用两条马尔科夫链进行更好的突然变化建模. 一项新的控制法确保了系统稳定性和干扰减弱,由达布克斯方程示例验证.
科学领域:
- 控制理论 控制理论
- 系统工程 系统工程
- 随机系统 随机系统 随机系统
背景情况:
- 传统的二维马尔科夫跳跃系统 (MJS) 经常因单个马尔科夫链的局限性而难以建模复杂,突然的变化.
- 模式模糊性是现有的二维MJS模型中常见的问题,阻碍了准确的现实应用.
研究的目的:
- 提出一种改进的跳跃模型,用于使用两个独立的马尔科夫链的罗塞型二维MJS.
- 制定一个双模式依赖的状态反控制法来稳定增强的2D MJS.
- 为了建立足够的标准来确定非对称平均平方稳定性和H∞干扰减弱.
主要方法:
- 一个新的2D跳跃模型,采用两个独立的马尔科夫链来实现水平和垂直动态.
- 双模式依赖的利亚普诺夫功能技术,以提高稳定性标准的可行性.
- 一个非保守的分离原理来推导等效条件,包括线性矩阵不等式 (LMIs).
主要成果:
- 拟议的2D跳跃模型提供了卓越的建模功能,并避免了模式模糊性.
- 导出了一个足够的标准,以获得非对称的平均平方稳定性和H∞干扰减弱.
- 为控制法设计开发了等效条件,包括LMI,通过Darboux方程示例进行验证.
结论:
- 新的2D跳跃模型和控制策略有效地稳定了2D MJS与突然的参数变化.
- 使用双独立的马尔科夫链可显著提高建模准确性,避免模式模两可.
- 基于LMI的凸式优化算法为这些系统设计强大的控制器提供了一个实用的方法.
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