留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

LPV模型的动态压缩测量辨识算法

邱棚 李鸣谦 姚旭日 翟光杰 王雪艳

邱棚, 李鸣谦, 姚旭日, 等 . 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. doi: 10.13700/j.bh.1001-5965.2018.0487
引用本文: 邱棚, 李鸣谦, 姚旭日, 等 . 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. doi: 10.13700/j.bh.1001-5965.2018.0487
QIU Peng, LI Mingqian, YAO Xuri, et al. Dynamic compression measurement identification algorithm of LPV model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(5): 961-969. doi: 10.13700/j.bh.1001-5965.2018.0487(in Chinese)
Citation: QIU Peng, LI Mingqian, YAO Xuri, et al. Dynamic compression measurement identification algorithm of LPV model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(5): 961-969. doi: 10.13700/j.bh.1001-5965.2018.0487(in Chinese)

LPV模型的动态压缩测量辨识算法

doi: 10.13700/j.bh.1001-5965.2018.0487
基金项目: 

国家自然科学基金 61605218

中国科学院国防科技创新基金 CXJJ-17S023

详细信息
    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

    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

    通讯作者:

    翟光杰, E-mail:gjzhai@nssc.ac.cn

  • 中图分类号: V19;TP271+.7

Dynamic compression measurement identification algorithm of LPV model

Funds: 

National Natural Science Foundation of China 61605218

National Defense Science and Technology Innovation Foundation of Chinese Academy of Sciences CXJJ-17S023

More Information
  • 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。

     

  • 图 1  LPV模型真值和不同算法辨识结果对比

    Figure 1.  Comparison between truth value of LPV model and identification result of different algorithms

    图 2  测量数对不同算法预测精度的影响

    Figure 2.  Influence of measurement number on prediction accuracy of different algorithms

    图 3  观测噪声对不同算法预测精度的影响

    Figure 3.  Influence of measurement noise on prediction accuracy of different algorithms

    图 4  线性变化情况下测量数对不同算法预测精度的影响

    Figure 4.  Influence of measurement number on output prediction accuracy of different algorithms in case of linear variation

  • [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. doi: 10.1109/TCST.2014.2327584
    [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. doi: 10.1016/j.ymssp.2017.07.054
    [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. doi: 10.3873/j.issn.1000-1328.2013.04.006

    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). doi: 10.3873/j.issn.1000-1328.2013.04.006
    [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. doi: 10.1016/j.automatica.2008.08.015
    [5] BAMIEB B, GIARRE L.Identification of linear parameter varying models[J].International Journal of Robust and Nonlinear Control, 2002, 12(9):841-853. http://cn.bing.com/academic/profile?id=2abde2438c1bbe5c175bac950031851c&encoded=0&v=paper_preview&mkt=zh-cn
    [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. doi: 10.1016/j.ymssp.2009.04.007
    [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. doi: 10.3182/20120711-3-BE-2027.00230
    [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. doi: 10.1109/TCST.2016.2642159
    [11] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory, 2006, 52(4):1289-1306. doi: 10.1109/TIT.2006.871582
    [12] CANDÈS E J, TAO T.Decoding by linear programming[J].IEEE Transactions on Information Theory, 2005, 51(12):4203-4215. doi: 10.1109/TIT.2005.858979
    [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. doi: 10.1109/TSP.2013.2289875
    [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. doi: 10.1109/MSP.2013.2279507
    [15] CANDÈS E J, ROMBERG J.Sparsity and incoherence in compressive sampling[J].Inverse Problems, 2006, 23(3):969-985. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_math%2f0611957
    [16] CANDÈS E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique, 2008, 346(9-10):589-592. doi: 10.1016/j.crma.2008.03.014
    [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. doi: 10.1190/geo2017-0321-TIOgeo.1
    [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. http://d.old.wanfangdata.com.cn/Periodical/wlxb201701009

    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). http://d.old.wanfangdata.com.cn/Periodical/wlxb201701009
    [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. doi: 10.1109/TIT.2010.2070191
    [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. doi: 10.1016/j.acha.2011.05.001
    [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. doi: 10.1007/s00365-007-9003-x
  • 加载中
图(4)
计量
  • 文章访问数:  646
  • HTML全文浏览量:  103
  • PDF下载量:  314
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-08-29
  • 录用日期:  2018-12-07
  • 网络出版日期:  2019-05-20

目录

    /

    返回文章
    返回
    常见问答