一个分数级高阶扩展的卡尔曼波器,用于分数级非线性系统
Wei Yu1, Yanxiang Zhang1, Rui Chen2
1School of Mechanical and Electrical Engineering and Automation, Foshan University, Foshan 528231, PR China.
ISA transactions
|March 1, 2026
概括
一个新的高阶分数扩展卡尔曼波器 (FHEKF) 增强了非线性系统的估计. 第三阶的泰勒扩展为分数顺序系统提供了最佳的及时性和有效的动态后续.
科学领域:
- 控制系统工程 控制系统工程
- 非线性动力学是一种非线性动力学.
- 估计理论估计理论
背景情况:
- 分数顺序非线性系统对传统状态估计技术提出了重大挑战.
- 现有的卡尔曼波器变体经常与高阶非线性和分数动态的复杂性作斗争.
- 准确的状态估计对于有效控制和监测这些系统至关重要.
研究的目的:
- 为分数级非线性系统开发一种新的高阶分数扩展卡尔曼波器 (FHEKF) 算法.
- 为了评估泰勒扩展的性能和最佳顺序,用于状态估计.
- 为了证明拟议的FHEKF在动力动态过程状态估计中的有效性.
主要方法:
- 将非线性函数扩展为高阶泰勒数列,使用估计误差作为变量.
- 定义高阶多项式术语作为隐藏变量,以建立相应的线性动态模型.
- 通过结合预测错误估计和状态预测来重建系统状态估计.
主要成果:
- 模拟实验确定了第三阶段的泰勒扩展,在第一到第四阶段的扩展中,它具有最高的及时性.
- 在动力动态过程估计中,FHEKF (第三顺序) 与其他三种过器相比,表现出优越的动态跟踪能力.
- 拟议的FHEKF在实验电机动态过程中表现出强大的抗干扰性能.
结论:
- 开发的FHEKF算法有效地解决了分数顺序非线性系统中的状态估计挑战.
- 第三级泰勒扩展提供了准确性和计算效率 (及时性) 之间的最佳平衡.
- FHEKF算法在现实应用中证明了其实用性和有效性,例如电机控制.
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