基于最小二乘支持向量机建模的混沌系统控制

提出了基于最小二乘支持向量机（LS-SVMs）建模的混沌系统控制方法.与前向神经网络相比，LS-SVMs的优点是其训练过程遵循结构风险最小化原则，不易发生过拟合现象；它通过解一组线性方程组可得到全局惟一的最优解；LS-SVMs的拓扑结构在训练结束时自动获得而不需要预先确定.该方法不需要被控混沌系统的解析模型，且当测量噪声存在情况下控制仍然有效.以一维和二维非线性映射为例进行数值仿真，表明该方法是有效和可行的.关键词：混沌控制支持向量机建模

Control of chaotic system based on least squares support vector machine modeling

A new approach to control chaotic systems is presented. This control approach is based on least squares support vector machines (LS_SVMs) modeling. Compared wit h the feed_forward neural networks, the LS_SVM possesses prominent advantages: o ver fitting is unlikely to occur by employing structural risk minimization crite rion, the global optimal solution can be uniquely obtained owing to the fact tha t its training is performed through the solution of a set of linear equations. A lso, the LS_SVM need not determine its topology in advance, which can be automat ically obtained when the training process ends. Thus the effectiveness and feasi bility of this method are found to be better than those of the feed_forward neur al networks. The method does not needs an analytic model, and it is still effect ive when there are measurement noises. The chaotic systems with one_and two_ dim ensional nonlinear maps are used as examples for demonstration.