基于数据的一类部分未知仿射非线性系统近似解

张国山; 王岩浩

doi:10.16383/j.aas.2015.c150272

基于数据的一类部分未知仿射非线性系统近似解

doi: 10.16383/j.aas.2015.c150272

张国山^,,
王岩浩

1.
天津大学电气与自动化工程学院天津 300072

基金项目:

国家自然科学基金(61074088, 61473202)资助

详细信息

作者简介:
王岩浩天津大学电气与自动化工程学院硕士研究生. 主要研究方向为机器学习, 数据驱动控制. E-mail: hhsnh2013@tju.edu.cn

通讯作者:
张国山天津大学电气与自动化工程学院教授. 主要研究方向为线性与非线性系统控制, 智能控制与混沌控制及应用. 本文通信作者. E-mail: zhanggs@tju.edu.cn

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- 文章访问数: 1467
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- 被引次数: 0
出版历程
- 收稿日期: 2015-05-11
- 修回日期: 2015-07-27
- 刊出日期: 2015-10-20

Data-based Approximate Solution for a Class of Affine Nonlinear Systems with Partially Unknown Functions

ZHANG Guo-Shan^,,
WANG Yan-Hao

1.
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072

Funds:

Supported by National Natural Science Foundation of China (61074088, 61473202)

摘要

摘要: 针对一类部分未知仿射非线性系统无穷区间求解问题,利用在线采样数据,提出了在线无偏最小二乘支持向量机(Least square support vector machines, LS-SVM)的方法. 首先,通过引入一个参数消除了LS-SVM的偏置项,避免了冗余计算,同时在优化目标中引入权值函数,对靠近当前时刻的数据样本点赋予更高权重,提高了计算精度; 其次,采用滚动时间窗的方法,实现非线性系统无穷区间求解,并满足求解实时性要求;最后,通过数值算例仿真验证了本文方法的有效性和优越性.
- 仿射非线性系统 /
- 数据驱动控制 /
- 最小二乘支持向量机 /
- 滚动时间窗 /
- 机器学习
Abstract: A new method named online unbiased least square support vector machines (LS-SVMs) is proposed by using online sampling data to find the approximate solution of a class of partially unknown affine nonlinear systems within the infinite interval. Firstly, we eliminate the bias of LS-SVMs by introducing a parameter to avoid redundant computation, meanwhile, we give the data points which are closer to the current moment more weights by introducing a weight function to the optimized target, thus the computational accuracy is improved. Secondly, the method of sliding time window is employed to achieve the approximate solution for affine nonlinear systems within the infinite interval and meet the requirement of real-time solving. Finally, simulations of numerical examples demonstrate the efficiency and superiority of the proposed method.
- Affine nonlinear system /
- data-driven control /
- least square support vector machines (LS-SVM) /
- sliding time window /
- machine learning

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参考文献(21)

[1]	Mohaqeqi M, Kargahi M, Dehghan M. Adaptive scheduling of real-time systems cosupplied by renewable and nonrenewable energy sources. ACM Transactions on Embedded Computing Systems (TECS), 2013, 13(1s): Article No.36
[2]	Yao W, Jiang L, Fang J K, Wen J Y, Cheng S J. Decentralized nonlinear optimal predictive excitation control for multi-machine power systems. International Journal of Electrical Power & Energy Systems, 2014, 55: 620-627
[3]	Qi G Y, Chen Z Q, Yuan Z Z. Adaptive high order differential feedback control for affine nonlinear system. Chaos, Solitons & Fractals, 2008, 37(1): 308-315
[4]	Khan Z H, Gu I Y H. Nonlinear dynamic model for visual object tracking on Grassmann manifolds with partial occlusion handling. IEEE Transactions on Cybernetics, 2013, 43(6): 2005-2019
[5]	Ramos J I. Linearization techniques for singular initial-value problems of ordinary differential equations. Applied Mathematics and Computation, 2005, 161(2): 525-542
[6]	Odibat Ζ Μ, Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation, 2006, 7(1): 27-34
[7]	Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. Courier Corporation, 2012.
[8]	Duan J S, Rach R, Baleanu D, Wazwaz A M. A review of the Adomian decomposition method and its applications to fractional differential equations. Communications in Fractional Calculus, 2012, 3(2): 73-99
[9]	Mall S, Chakraverty S. Numerical solution of nonlinear singular initial value problems of Emden-Fowler type using Chebyshev neural network method. Neurocomputing, 2015, 149: 975-982
[10]	Hou Zhong-Sheng, Xu Jian-Xin. On data-driven control theory: the state of the art and perspective. Acta Automatica Sinica, 2009, 35(6): 650-667(侯忠生, 许建新. 数据驱动控制理论及方法的回顾和展望. 自动化学报, 2009, 35(6): 650-667)
[11]	Suykens J A K, Vandewalle J. Least squares support vector machine classifiers. Neural Processing Letters, 1999, 9(3): 293-300
[12]	Zhang G S, Wang S W, Wang Y M, Liu W Q. LS-SVM approximate solution for affine nonlinear systems with partially unknown functions. Journal of Industrial and Management Optimization, 2014, 10(2): 621-636
[13]	Yan Wei-Wu, Chang Jun-Lin, Shao Hui-He. Least square SVM regression method based on sliding time window and its simulation. Journal of Shanghai Jiaotong University, 2004, 38(4): 524-526, 532(阎威武, 常俊林, 邵惠鹤. 基于滚动时间窗的最小二乘支持向量机回归估计方法及仿真. 上海交通大学学报, 2004, 38(4): 524-526, 532)
[14]	Zhou Xin-Ran, Teng Zhao-Sheng. An online sparse LSSVM and its application in system modeling. Journal of Hunan University (Natural Sciences), 2010, 37(4): 37-41(周欣然, 滕召胜. 一种在线稀疏LSSVM及其在系统建模中的应用. 湖南大学学报(自然科学版), 2010, 37(4): 37-41)
[15]	Cai Yan-Ning, Hu Chang-Hua. Dynamic non-bias LS-SVM learning algorithm based on Cholesky factorization. Control and Decision, 2008, 32(12): 1363-1367(蔡艳宁, 胡昌华. 一种基于Cholesky分解的动态无偏LS-SVM学习算法. 控制与决策, 2008, 32(12): 1363-1367)
[16]	Vapnik V. The Nature of Statistical Learning Theory (2nd edition). New York: Springer Science & Business Media, 2000.
[17]	Lázaro M, Santamaría I, Pérez-Cruz F, Artés-Rodríguez A. Support vector regression for the simultaneous learning of a multivariate function and its derivatives. Neurocomputing, 2005, 69(1-3): 42-61
[18]	Mehrkanoon S, Falck T, Suykens J A K. Approximate solutions to ordinary differential equations using least squares support vector machines. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(9): 1356-1367
[19]	Cawley G C, Talbot N L C. Fast exact leave-one-out cross-validation of sparse least-squares support vector machines. Neural Networks, 2004, 17(10): 1467-1475
[20]	El-Tawil M A, Bahnasawi A A, Abdel-Naby A. Solving Riccati differential equation using Adomian's decomposition method. Applied Mathematics and Computation, 2004, 157(2): 503-514
[21]	Lagaris I E, Likas A, Fotiadis D I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks, 1998, 9(5): 987-1000

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基于数据的一类部分未知仿射非线性系统近似解

doi: 10.16383/j.aas.2015.c150272

作者简介:
王岩浩天津大学电气与自动化工程学院硕士研究生. 主要研究方向为机器学习, 数据驱动控制. E-mail: hhsnh2013@tju.edu.cn

通讯作者:
张国山天津大学电气与自动化工程学院教授. 主要研究方向为线性与非线性系统控制, 智能控制与混沌控制及应用. 本文通信作者. E-mail: zhanggs@tju.edu.cn

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Data-based Approximate Solution for a Class of Affine Nonlinear Systems with Partially Unknown Functions

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留言板

基于数据的一类部分未知仿射非线性系统近似解

doi: 10.16383/j.aas.2015.c150272

作者简介: 王岩浩 天津大学电气与自动化工程学 院硕士研究生. 主要研究方向为机器学 习, 数据驱动控制. E-mail: hhsnh2013@tju.edu.cn

通讯作者: 张国山 天津大学电气与自动化工程学 院教授. 主要研究方向为线性与非线性 系统控制, 智能控制与混沌控制及应用. 本文通信作者. E-mail: zhanggs@tju.edu.cn

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出版历程

Data-based Approximate Solution for a Class of Affine Nonlinear Systems with Partially Unknown Functions

计量

出版历程

目录

作者简介:
王岩浩天津大学电气与自动化工程学院硕士研究生. 主要研究方向为机器学习, 数据驱动控制. E-mail: hhsnh2013@tju.edu.cn

通讯作者:
张国山天津大学电气与自动化工程学院教授. 主要研究方向为线性与非线性系统控制, 智能控制与混沌控制及应用. 本文通信作者. E-mail: zhanggs@tju.edu.cn