Nonlinear control systems modelling: global vs. local

Two nonlinear control systems modelling methodologies are presented and compared. The nonlinear system is given in the form of a NARX model. One modelling method is based on decomposition of the nonlinear function (right-hand side of the NARX model) into multiple local linear mappings, while the second takes the global approach by using a modified Fourier series technique. The local mappings are represented by a self-organising neural network and a local linear mapping is associated with each neuron. The network is trained by a combination of vector quantisation and winner takes most procedure. The global approach is based on a nonuniform multidimensional sampling theory. It replaces the original nonuniform sampling problem in the space domain by the uniform sampling problem in the frequency domain. The application of the proposed methods to modelling of nonlinear control systems is also given.