基于鲁棒优化的系统辨识算法研究

钱富才; 黄姣茹; 秦新强

doi:10.3724/SP.J.1004.2014.00988

基于鲁棒优化的系统辨识算法研究

doi: 10.3724/SP.J.1004.2014.00988

1.
西安理工大学自动化与信息工程学院西安 710048;
2.
西安工业大学新型网络与检测控制国家地方联合工程实验室西安 710032;
3.
西安理工大学理学院西安 710054

基金项目:

国家自然科学基金（61273127），高等学校博士学科点专项科研基金（20116118110008）资助

详细信息

作者简介:
黄姣茹西安理工大学自动化与信息工程学院博士研究生. 主要研究方向为鲁棒优化，系统辨识和最优控制. E-mail：huangjiaoru@126.com

计量
- 文章访问数: 2513
- HTML全文浏览量: 117
- PDF下载量: 1044
- 被引次数: 0
出版历程
- 收稿日期: 2013-04-08
- 修回日期: 2013-08-12
- 刊出日期: 2014-05-20

Research on Algorithm for SystemIdentification Based on RobustOptimization

1.
School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048;
2.
The Notional-Local Joint Engineering Laboratory for New Network and Detection Control, Xi'an Technological University, Xi'an 710032;
3.
School of Science, Xi'an University of Technology, Xi'an 710054

Funds:

Supported by National Natural Science Foundation of China (61273127), and Specialized Research Fund for the Doctoral Program of Higher Education (20116118110008)

摘要

摘要: 输入-输出数据是解决系统辨识问题的关键要素，传统的辨识理论除了假定影响输入-输出数据干扰的密度函数已知外，还要假定输入-输出数据能够精确获得，完全忽略了所用数据的质量.本文突破了传统理论的两个假设，首先用工程上易于获得的干扰的有界集合代替干扰的密度函数，并在特定数据不确定性结构下，考虑了数据质量问题，然后，以半定规划为基础，导出了鲁棒对等式，从而将系统辨识转化为对数据质量具有鲁棒性的优化问题，通过求解该优化问题，得到了一种新的鲁棒优化辨识方法，仿真结果表明了新方法的可行性和有效性.
- 系统辨识 /
- 不确定性 /
- 鲁棒优化 /
- 半定规划
Abstract: Input-output data is a key element in solving the problem of system identification. The traditional identification theory takes into account the assumptions that the density function of the disturbance is known and the input-output data can be accurately obtained, while completely ignores the quality of the data used. In the paper, to overcom the limitation of the two assumptions, a bounded set is firstly taken which can be obtained easily in engineering as an alternative to the density function. Subsequently, with the specific uncertain data structure and considering the effect of the data quality, robust counterpart is derived by the semi-definite programming theory. And, the system identification problem is converted to an optimization problem which is robust to the uncertain data. By solving the optimization problem, a new identification algorithm based on robust optimization is proposed. Simulation results show the feasibility and effectiveness.
- System identification /
- uncertainty /
- robust optimization /
- semi-definite programming

HTML全文

参考文献(21)

[1]	Fang Chong-Zhi, Xiao De-Yun. Process Identification. Beijing: Tsinghua University Press, 1998(方崇智, 萧德云. 过程辨识. 北京: 清华大学出版社, 1988)
[2]	Ljung L. System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, 1987
[3]	Chen H F. Recursive identification for Wiener model with discontinuous piece-wise linear function. IEEE Transactions on Automatic Control, 2006, 51(3): 390-400
[4]	Burnham K P, Anderson D R. Multimodel inference: understandingAIC and BIC in model selection. Sociological Methods and Research, 2004, 33(2): 261-304
[5]	Soderstrom T. Accuracy analysis of the Frisch scheme for identifying errors-in-variables systems. IEEE Transactions on Automatic Control, 2007, 52(6): 985-997
[6]	Kar S, Sinopli B, Moura J M F. Kalman filtering with intermittent observations: weak convergence to a stationary distribution. IEEE Transactions on Automatic Control, 2012,57(2): 405-420
[7]	Ge Quan-Bo, Li Wen-Bin, Sun Ruo-Yu, Xu Zi. Centralized fusion algorithms based on EKF for multisenor non-linear systems.Acta Automatica Sinica, 2013, 39(6): 816-825(葛全波, 李文斌, 孙若愚, 徐姿. 基于EKF的集中式融合估计研究.自动化学报, 2013, 39(6): 816-825)
[8]	Li D, Qian F C, Fu P L. Variance minimization approach for a class of dual control problems. IEEE Transactions on Automatic Control, 2002, 47(12): 2010-2020
[9]	Li D, Qian F C, Fu P L. Optimal nominal dual control for discrete-time LQG problem with unknown parameters. Automatica, 2008, 44(1): 119-127
[10]	Li D, Qian F C, Gao J J. Performance-first control for discrete-time LQG problems. IEEE Transactions on Automatic Control, 2009, 54(9): 2225-2230
[11]	Qian F C, Gao J J, Li D. Complete statistical characterization of discrete-time LQG and cumulant control. IEEE Transactions on Automatic Control, 2012, 57(8):2110-2115
[12]	Ben-Tal A, Nemirovski A. Robust optimization: methodology and applications. Mathematical Programming, 2002, 92(3): 453-480
[13]	Lin Xiao-Zhong, Xie Lei, Su Hong-Ye. Economic performance for predict control system under model uncertainty. Acta Automatica Sinica,2012,38(8): 1-5(林晓钟, 谢磊, 苏宏业. 模型不确定条件下预测控制经济性能评估的研究.自动化学报, 2012, 38(8):-5)
[14]	Bertsimas D, Litvinov E, Sun X A, Zhao J Y, Zheng T X. Adaptive robust optimizaition for the security constrained unit commitment problem. IEEE Transactions on Power Systems, 2013, 28(1): 52-63
[15]	Soyster A L. Convex programming with set-inclusive constraints and applications to inexact linear programming. Operational Research, 1973, 21: 1154-1157
[16]	Ben-Tal A, Nemirovski A. Robust convex optimization. Mathematics of Operations Research, 1998, 23(4):769-805
[17]	Bandi C, Bertsimas D. Tracable stochastic analysis in high dimensions via robust optimization. Mathematical Programming, 2012, 134(1): 23-70
[18]	Wang Le-Yi, Zhao Wen-Xiao. System identification: new paradigms, challenges, and opportunities. Acta AutomaticaSinica,2013, 39(7): 933-942(王乐一, 赵文虓. 系统辨识: 新的模式、挑战及机遇. 自动化学报, 2013,39(7): 933-942)
[19]	Ben-Tal A, Nemirovski A. Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 2000, 88(3): 411-424
[20]	Ben-Tal A, Nemirovski A. Robust solutions of uncertain linear programs. Operations Research Letters, 1999, 25:1-13
[21]	El-Ghaoui L, Lebret H. Robust solutions to least-squares problems with uncertain data. SIAM Journal on Matrix Analysis and Applications, 1997, 18: 1035-1064