Tradeoff between Approximation Accuracy and Complexity: HOSVD Based Complexity Reduction

Abstract

Higher Order Singular Value Decomposition (HOSVD) based complexity reduction method is proposed in this paper to polytopic model approximation techniques. The main motivation is that the polytopic model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of local linear models. The reduction technique proposed here is capable of defining the contribution of each local linear model, which serves to remove the weakly contributing ones according to a given threshold. Reducing the number of local models leads directly to the complexity reduction. The proposed reduction can also be performed on TS fuzzy model approximation method. A detailed illustrative example of a non-linear dynamic model is also discussed. The main contribution of this paper is the multi-dimensional extension of the SVD reduction technique introduced in the preliminary work [1]. The advantage of this extension is that the HOSVD based technique of this paper can be applied to polytopic models varying in a multi-dimensional parameter space unlike the reduction method of [1] which is designed for one dimensional parameter space.