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 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.