Adaptive local model networks with higher degree polynomials

A new adaptation method for local model networks with higher degree polynomials which are trained by the polynomial model tree (POLYMOT) algorithm is presented in this paper. Usually the local models are linearly parameterized and those parameters are typically adapted by a recursive least squares approach. For the utilization of higher degree polynomials a subset selection method, which is a part of the POLYMOT algorithm, selects and estimates the most significant parameters from a huge parameter matrix. This matrix contains one parameter w_{i, nx} for each input u^l_p up to the maximal polynomial degree and for all the combinations of the inputs. It is created during the training procedure of the local model network. For the online adaptation of the trained local model network only the selected parameters should be used. Otherwise the local model network would be too flexible and the idea of subset selection would be lost. Therefore the presented adaptation method generates at first a new parameter matrix with the selected and most significant parameters which are unequal to zero. Afterwards the local model parameters can be adapted with the aid of a standard recursive least squares method.