Support-Vector-based Least Squares for learning non-linear dynamics

A function approximator is introduced in this paper that is based on Least Squares Support Vector Machines (LSSVM) and on Least Squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar as with LSSVM. By selecting these as indicator functions the indicators for LS can be interpret in a support vector machine setting and the curse of dimensionality can be circumvented. The indicators are included by a forward selection scheme. This makes the computational load for the training phase small. As long as the function is not approximated good enough, and the function is not overfitting the data, a new indicator is included. To test the approximator the inverse non-linear dynamics of a linear motor are learnt. This is done by including the approximator as learning mechanism in a learning feed-forward controller.