An Efficient Algorithm for the Tensor Product Model Transformation

The tensor-product (TP) model transformation was proposed recently as a numerical and automatically executable method which is capable of transforming linear parameter varying (LPV) state-space models into the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. The crucial disadvantage of the TP model transformation is that its computational load explodes with the density of discretization and the dimensionality of the parameter vector of the parameter-varying state-space model. In this paper we propose a new algorithm that leads to considerable reduction of the computation in the TP model transformation. The main idea behind the modified algorithm is to minimize the number of discretized points to acquire as much information as possible. The modified TP model transformation can readily be executed on a regular computer efficiently and concisely, especially in higher dimensional cases when the original TP model transformation fails. The paper also presents numerical examples to show the effectiveness of the new algorithm.