北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (5): 961-969.doi: 10.13700/j.bh.1001-5965.2018.0487

• 论文 • 上一篇    下一篇

LPV模型的动态压缩测量辨识算法

邱棚1,2, 李鸣谦1,2, 姚旭日2, 翟光杰2, 王雪艳3   

  1. 1. 中国科学院国家空间科学中心, 北京 100190;
    2. 中国科学院大学, 北京 100049;
    3. 北京信息科技大学 机电工程学院, 北京 100192
  • 收稿日期:2018-08-29 出版日期:2019-05-20 发布日期:2019-05-21
  • 通讯作者: 翟光杰.E-mail:gjzhai@nssc.ac.cn E-mail:gjzhai@nssc.ac.cn
  • 作者简介:邱棚 男,博士研究生。主要研究方向:压缩感知、系统辨识、模型预测控制;李鸣谦 男,博士研究生。主要研究方向:超声成像、声音定位;姚旭日 男,副研究员。主要研究方向:鬼成像、超分辨成像、压缩成像;翟光杰 男,研究员。主要研究方向:极弱光探测、计算成像、微重力科学;王雪艳 女,高级实验师。主要研究方向:机器人运动控制、控制器设计。
  • 基金资助:
    国家自然科学基金(61605218);中国科学院国防科技创新基金(CXJJ-17S023)

Dynamic compression measurement identification algorithm of LPV model

QIU Peng1,2, LI Mingqian1,2, YAO Xuri2, ZHAI Guangjie2, WANG Xueyan3   

  1. 1. National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China;
    2. University of Chinese Academy of Sciences, Beijing 100049, China;
    3. Mechanical Electrical Engineering School, Beijing Information Science and Technology University, Beijing 100192, China
  • Received:2018-08-29 Online:2019-05-20 Published:2019-05-21

摘要: 在解决线性参变(LPV)模型的辨识问题上,最小二乘算法以结构简单、计算复杂度低等优点被大量使用。但最小二乘算法辨识结果受制于计算精度和模型近似精度,而这两者在同一个系统中是互斥的。因此,该算法的辨识结果与真值总是存在一定的误差。另外,在高阶LPV模型辨识或采样成本高的情况下,一般模型参数要多于辨识数据,而此时最小二乘算法很难得到稳定的辨识结果。本文提出的动态压缩测量辨识(DCMI)算法从两个方面提高在该情况下的系统辨识精度。其一,利用“匀速变化”及“非匀速变化”模型表示参变函数,以提高模型近似精度。其二,利用压缩感知理论的欠采样能力,在同等数据量的情况下提高参数的计算精度、扩大模型的计算规模。仿真结果表明,基于“匀速变化”模型DCMI算法可以准确地辨识出LPV函数,而且该算法在辨识数据不足的情况下仍然能够获得稳定的辨识结果。

关键词: 系统辨识, 压缩感知, 线性参变(LPV), 线性时变(LTV), 正交匹配追踪(OMP)

Abstract: In solving the identification problem of linear parametric variation (LPV) model, the least squares algorithm is widely used due to the advantages of simple structure and low computational complexity. However, the results of least squares algorithm are subject to computational accuracy and model approximation accuracy, which are mutually exclusive in the same system. Therefore, there is always a certain error between the identification result and the true value of the algorithm. In addition, in the case of high-order LPV model identification or high sampling cost, the general model parameters are much more than the identification data. Consequently, it is difficult for the least squares algorithm to obtain stable identification results. The dynamic compression measurement identification (DCMI) algorithm proposed in this paper improves the system identification accuracy in this case from two aspects. First, the "uniform motion" and "non-uniform motion" models are used to represent the parametric function to improve the approximate accuracy of the model. Second, the under-sampling ability of the compressed sensing theory is utilized to improve the calculation accuracy of the parameters and expand the calculation scale of the model in the case of the same amount of data. The simulation results show that the proposed DCMI algorithm based on the "uniform motion" model can accurately identify the linear parametric function. Even in the case of insufficient identification data, the algorithm can still obtain stable identification results.

Key words: system identification, compressed sensing, linear parametric variation (LPV), linear time-variant (LTV), orthogonal matching pursuit (OMP)

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