采样数据模糊 [公式:参见文本] 估计器用于控制非线性抛物线偏微分方程
M Sivakumar1, S Dharani2, Jinde Cao3
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India. sivakumar.m@vit.ac.in.
Scientific reports
|February 14, 2026
概括
这项研究为带有干扰的非线性局部微分系统提供了一个强大的采样数据模糊控制方法. 该研究设计了一个基于模糊估计器的控制器来稳定这些系统,确保对外部干扰的弹性.
科学领域:
- 控制理论 控制理论
- 非线性系统分析 非线性系统分析
- 部分微分方程 部分微分方程
背景情况:
- 非线性局部微分系统 (NPDS) 由于其复杂性和固有的动力学,难以控制.
- 塔卡吉-苏杰诺 (T-S) 模糊模型有效地代表了广泛的非线性系统,包括抛物线部分微分系统.
- 在NPDS中的干扰可以显著降低系统的性能和稳定性,需要强大的控制策略.
研究的目的:
- 为受干扰的非线性抛物线局部微分系统开发一个强大的采样数据模糊控制策略.
- 设计一个基于模糊估计器的控制器,能够稳定闭环系统,同时承受特定水平的干扰.
- 提供一个系统的设计方法,使用线性矩阵不等式 (LMIs) 进行强大的稳定.
主要方法:
- 使用Takagi-Sugeno (T-S) 模糊框架建模非线性抛物线局部微分系统.
- 运用利亚普诺夫稳定理论,格林公式和不平等技术进行稳定性分析.
- 制定强大的稳定问题作为一组线性矩阵不等式 (LMIs) 控制器合成.
主要成果:
- 一个强大的基于模糊估计器的采样数据控制器被设计用于稳定TS模糊闭环部分微分系统.
- 导出的标准有效地解决了强大的稳定设计问题,考虑到扩散和控制的影响.
- 建议标准的可行性使用MATLAB LMI控制工具箱进行了验证.
结论:
- 拟议的采样数据模糊控制方法在存在干扰的情况下有效稳定非线性局部微分系统.
- 基于LMI的设计方法提供了一个可计算的解决方案,用于对复杂系统进行可靠的控制.
- 模拟结果证实了开发的标准和拟议的控制策略的有效性.
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