Identification and Control of Discrete-Time Nonlinear Systems Using Affine Support Vector Machines
Identification and Control of Discrete-Time Nonlinear Systems Using Affine Support Vector Machines
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DOI：
10.1142/s0218213009000469
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发表时间：
2009-12
期刊：
影响因子：
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通讯作者：
Li Zhang;Y. Xi;Weida Zhou
中科院分区：
文献类型：
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作者：
Li Zhang;Y. Xi;Weida Zhou
支持向量机（SVM）是一种通用的学习方法。本文提出了一种用于回归的仿射支持向量机（ASVM），用于输入仿射非线性模型的辨识与控制。ASVM是SVM的一个变种，继承了SVM的优点。ASVM的解决方案被转换成一个凸二次规划（QP）。因此，ASVM拥有独特的全球解决方案。此外，由于ASVM对数据的维数不敏感，因此避免了维数灾难。非线性系统的常用模型是非线性自回归外生（NARX）模型。如果NARX模型能很好地表示为输入仿射非线性模型，则ASVM在辨识和控制方面都能获得良好的性能。实验结果验证了ASVM在离散时间非线性系统辨识与控制中的有效性。
Support vector machine (SVM) is a universal learning method. In this paper, an affine support vector machine (ASVM) for regression is presented for identification and control of input-affine nonlinear models. ASVM is a variant of SVM and so inherits its merits. The solution to ASVM is cast into a convex quadratic programming (QP). Hence ASVM has a unique global solution. In addition, the curse of dimensionality is avoided because ASVM is insensitive to the dimensionality of data. A commonly used model for a nonlinear system is a nonlinear autoregressive exogenous (NARX) model. ASVM could get good performance in both identification and control if a NARX model can be well represented by an input-affine nonlinear model. The experimental results validate the efficiency of ASVM in identification and control of discrete-time nonlinear systems.