LPV模型的动态压缩测量辨识算法

doi:10.13700/j.bh.1001-5965.2018.0487

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

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. 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 Peng^1,2, LI Mingqian^1,2, YAO Xuri², ZHAI Guangjie², WANG Xueyan³

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/Abstract

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)

中图分类号:

邱棚, 李鸣谦, 姚旭日, 翟光杰, 王雪艳. LPV模型的动态压缩测量辨识算法[J]. 北京航空航天大学学报, 2019, 45(5): 961-969.

QIU Peng, LI Mingqian, YAO Xuri, ZHAI Guangjie, WANG Xueyan. Dynamic compression measurement identification algorithm of LPV model[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2019, 45(5): 961-969.

参考文献

[1] HOFFMANN C,WERNER H.A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations[J].IEEE Transactions on Control Systems Technology,2015,23(2):416-433.
[2] TURK D,GILLIS J,PIPELEERS G,et al.Identification of linear parameter-varying systems:A reweighted l2,1-norm regularization approach[J].Mechanical Systems and Signal Processing,2018,100:729-742.
[3] 王明昊,刘刚,赵鹏涛,等.高超声速飞行器的LPV变增益状态反馈H_∞控制[J].宇航学报,2013,34(4):488-495.WANG M H,LIU G,ZHAO P T,et al.LPV H_∞ control for hypersonic vehicle[J].Journal of Astronautics,2013,34(4):488-495(in Chinese).
[4] VAN J W,VERHAEGEN M.Subspace identification of bilinear and LPV systems for open-and closed-loop data[J].Automatica,2009,45(2):372-381.
[5] BAMIEB B,GIARRE L.Identification of linear parameter varying models[J].International Journal of Robust and Nonlinear Control,2002,12(9):841-853.
[6] DE CAIGNY J,CAMINO J F,SWEVERS J.Interpolating model identification for SISO linear parameter-varying systems[J].Mechanical Systems and Signal Processing,2009,23(8):2395-2417.
[7] TOTH R,LYZELL C,ENQVIST M,et al.Order and structural dependence selection of LPV-ARX models using a nonnegative garrote approach[C]//Proceedings of the 48h IEEE Conference on Decision and Control(CDC)Held Jointly with 200928th Chinese Control Conference.Piscataway,NJ:IEEE Press,2009:7406-7411.
[8] ROJAS C R,HJALMARSSON H.Sparse estimation based on a validation criterion[C]//Proceedings of 201150th IEEE Conference on Decision and Control and European Control Conference.Piscataway,NJ:IEEE Press,2011:2825-2830.
[9] LAURAIN V,TOTH R,ZHENG W X,et al.Nonparametric identification of LPV models under general noise conditions:An LS-SVM based approach[J].IFAC Proceedings Volumes,2012,45(16):1761-1766.
[10] GOLABI A,MESKIN N,TOTH R,et al.A Bayesian approach for LPV model identification and its application to complex processes[J].IEEE Transactions on Control Systems Technology,2017,25(6):2160-2167.
[11] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[12] CANDōS E J,TAO T.Decoding by linear programming[J].IEEE Transactions on Information Theory,2005,51(12):4203-4215.
[13] ROSSI M,HAIMOVICH A M,ELDAR Y C.Spatial compressive sensing for MIMO radar[J].IEEE Transactions on Signal Processing,2014,62(2):419-430.
[14] WILLETT R M,DUARTE M F,DAVENPORT M A,et al.Sparsity and structure in hyperspectral imaging[J].IEEE Signal Processing Magazine,2014,31(1):116-126.
[15] CANDōS E J,ROMBERG J.Sparsity and incoherence in compressive sampling[J].Inverse Problems,2006,23(3):969-985.
[16] CANDōS E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9-10):589-592.
[17] PATI Y C,REZAⅡFAR R,KRISHNAPRASAD P S.Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition[C]//Proceedings of Conference Record of the 27th Asilomar Conference on Signals,Systems and Computers.Piscataway,NJ:IEEE Press,2002:40-44.
[18] LI C,ZHANG F.AVA inversion based on the L1-norm-based likelihood function and the total variation regularization constraint[J].Geophysics,2017,82(3):1-54.
[19] 王盼盼,姚旭日,刘雪峰,等.基于行扫描测量的运动目标压缩成像[J].物理学报,2017, 66(1):76-83.WANG P P,YAO X R,LIU X F,et al.Motion target imaging using compress sensing[J].Acta Physic Sinica,2017, 66(1):76-83(in Chinese).
[20] HAUPT J,BAJWA W U,RAZ G,et al.Toeplitz compressed sensing matrices with applications to sparse channel estimation[J].IEEE Transactions on Information Theory,2010,56(11):5862-5875.
[21] RAUHUT H,ROMBERG J,TROPP J A.Restricted isometries for partial random circulant matrices[J].Applied and Computational Harmonic Analysis,2012,32(2):242-254.
[22] BARANIUK R,DAVENPORT M,DEVORE R,et al.A simple proof of the restricted isometry property for random matrices[J].Constructive Approximation,2008,28(3):253-263.

LPV模型的动态压缩测量辨识算法

Dynamic compression measurement identification algorithm of LPV model

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	武梅丽文, 陈铭, 王放. 悬停状态下小型无人直升机飞行动力学模型辨识[J]. 北京航空航天大学学报, 2019, 45(3): 546-559.
[2]	薛倩, 刘婧, 马敏, 王化祥. 基于原始对偶内点法的EST图像重建[J]. 北京航空航天大学学报, 2019, 45(10): 1973-1981.
[3]	肖沈阳, 金志刚, 苏毅珊, 武晋. 压缩感知OFDM稀疏信道估计导频设计[J]. 北京航空航天大学学报, 2018, 44(7): 1447-1453.
[4]	贾伟州, 彭靖波, 谢寿生, 刘云龙, 李腾辉, 何大伟. 非线性多项式模型结构与参数一体化辨识[J]. 北京航空航天大学学报, 2018, 44(6): 1303-1311.
[5]	王彩云, 何志勇, 宫俊. 基于压缩感知的单脉冲雷达欺骗干扰机研究[J]. 北京航空航天大学学报, 2017, 43(9): 1789-1797.
[6]	聂静, 苏东林, 李红裔, 赵迪. 电路测试响应信号的GP-KSVD稀疏重构算法[J]. 北京航空航天大学学报, 2017, 43(7): 1336-1347.
[7]	蔺鲁萍, 王永革. 不完全角度CT图像重建的模型与算法[J]. 北京航空航天大学学报, 2017, 43(4): 823-830.
[8]	张立峰. 压缩感知在电容层析成像中的应用[J]. 北京航空航天大学学报, 2017, 43(11): 2316-2321.
[9]	刘浩强, 赵洪博, 冯文全. 基于CS的正则化稀疏度变步长自适应匹配追踪算法[J]. 北京航空航天大学学报, 2017, 43(10): 2109-2117.
[10]	谷晓鹏, 谢树果, 郝旭春. 基于压缩感知的近距离电磁辐射源定位方法[J]. 北京航空航天大学学报, 2017, 43(1): 79-85.
[11]	易可夫, 王东豪, 万江文. 基于优化字典学习算法的压缩数据收集[J]. 北京航空航天大学学报, 2016, 42(6): 1203-1209.
[12]	刘春辉, 齐越, 丁文锐, 张文秋. 最大相关熵准则自适应滤波器的分数阶长算法[J]. 北京航空航天大学学报, 2016, 42(2): 413-420.
[13]	刘海涛, 张智美, 成玮, 张学军. 联合压缩感知与干扰白化的脉冲干扰抑制方法[J]. 北京航空航天大学学报, 2015, 41(8): 1367-1373.
[14]	程艳合, 杨文革. 基于压缩感知的DSSS信号双阶段捕获方法[J]. 北京航空航天大学学报, 2015, 41(4): 624-631.
[15]	吕方旭, 张金成, 王泉, 王钰. 基于傅里叶基的自适应压缩感知重构算法[J]. 北京航空航天大学学报, 2014, 40(4): 544-550.