Piecewise linear networks (PLN) for process control

Abstract

General nonlinear system identification in practice is still an unsolved problem. The method proposed is an easy user-friendly way of combining classical linear system theory with modern soft computing methods. According to the non-linearity of the process being modelled one or more partitions of the input space are determined by a special type of neural network - piecewise linear networks (PLNs). For each partition a linear mapping is performed by the neural network with direct weighted connections from the input to the output neurons. There is a 3D weight matrix between the input, hidden and output layer. Neuron pruning improves the generalization. After the training phase the linear system matrices of the identified process can easily be extracted. For each linear system matrix an automatic procedure exists that creates the matrices for a linear state controller. The different matrices of the state controllers replace the matrices of the system equations in the PLN. This modified network is a Sugeno-Takagi controller that couples the different linear controllers by fuzzy logic. As an application a switched reluctance motor control is shown.