基于最小二乘支持向量机建模的混沌系统控制

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

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 。

A new approach to control chaotic systems is presented. This control approach is based on least squares support vector machines (LS-SVMs) modeling. Compared with the feed-forward neural networks, the LS-SVM possesses prominent advantages: over fitting is unlikely to occur by employing structural risk minimization criterion, the global optimal solution can be uniquely obtained owing to the fact that its training is performed through the solution of a set of linear equations. Also I the LS-SVM need not determine its topology in advance, which can be automatically obtained when the training process ends. Thus the effectiveness and feasibility of this method are found to be better than those of the feed-forward neural networks. The method does not needs an analytic model, and it is still effective when there are measurement noises. The chaotic systems with one-and two-dimensional nonlinear maps are used as examples for demonstration.