PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less Overbounding

Abstract

This brief presents a method for an automated generation of improved representations of linear parameter varying (LPV) systems, which is based on principal component analysis applied to typical scheduling trajectories. The procedure can help to reduce the conservatism in controller design by finding tighter regions in the space of scheduling parameters that contain the set of given trajectories. In addition, this method allows to determine approximations of LPV models with a reduced number of parameters and facilitates a systematic tradeoff between the number of parameters and the desired accuracy of the model. The proposed technique is illustrated by the application to a model of a two-link robot. Performance achieved with the controller designed using the reduced model is compared with those obtained by a robust control approach.