The control of nonlinear systems is a challenging task in particular in high dimensions. The approach of "gain scheduling" provides a general solution by combining linear control laws adapted to the current regime of the system. A numerical realization, however, is only possible for a moderate number of reference regimes or, in other words, for a parametrization of the dynamics by a moderate number of scheduling variables.

The purpose of our research is to develop a scheduling dimension reduction method using a clustering model based on neural networks.

The idea is as follows. The general nonlinear system is embedded in the class of so-called linear parameter varying (LPV) systems. In order to manage a nonlienar term efficiently, affine linear LPV systems are used and low dimensional scheduling variables are identified on the base of clusters in the system states.